2500 is breakfast to a 2700
Is there any chance that a 1300 rated player can beat a 2700 rated player?

most people agree it can happen, the argument is mostly split between those who think:
1)Since theres some chance, it may happen
2)The chance is so small, it may be there, but will never happen in 90x10^1000000 years, so the small chance that exists is irrelevant.
obviously that chance was an exagretation btw, just as a disclaimer to those who take things too seriously.

yeah but the OPs question was "is there any chance" so there is no room for interpretation. the answer is yes:)

For a serious answer. About 35 years ago, when I was rated in the 1400s, I had a very good tournament game against a 2500 player (USCF). The game was even, but I lost on time. It was a complex position. It was before computers, so I have never put it up to see how the computer viewed it. So I think it is possible to get a decent game anyway.
Haha, funny story

Let's be realistic. We know the names of every player rated 2700+. These are not ordinary Grandmasters; these are the top 51 players in the world.
Rank | Name | Title | Country | Rating | Games | B-Year |
1 | Carlsen, Magnus | g | NOR | 2843 | 0 | 1990 |
2 | Aronian, Levon | g | ARM | 2821 | 10 | 1982 |
3 | Kramnik, Vladimir | g | RUS | 2795 | 9 | 1975 |
4 | Radjabov, Teimour | g | AZE | 2792 | 9 | 1987 |
5 | Nakamura, Hikaru | g | USA | 2786 | 9 | 1987 |
6 | Karjakin, Sergey | g | RUS | 2780 | 10 | 1990 |
7 | Anand, Viswanathan | g | IND | 2780 | 0 | 1969 |
8 | Caruana, Fabiano | g | ITA | 2772 | 9 | 1992 |
9 | Ivanchuk, Vassily | g | UKR | 2771 | 10 | 1969 |
10 | Morozevich, Alexander | g | RUS | 2758 | 0 | 1977 |
11 | Kamsky, Gata | g | USA | 2755 | 11 | 1974 |
12 | Grischuk, Alexander | g | RUS | 2752 | 11 | 1983 |
13 | Topalov, Veselin | g | BUL | 2751 | 10 | 1975 |
14 | Mamedyarov, Shakhriyar | g | AZE | 2748 | 10 | 1985 |
15 | Wang, Hao | g | CHN | 2748 | 10 | 1989 |
16 | Svidler, Peter | g | RUS | 2747 | 0 | 1976 |
17 | Gashimov, Vugar | g | AZE | 2737 | 0 | 1986 |
18 | Gelfand, Boris | g | ISR | 2736 | 8 | 1968 |
19 | Ponomariov, Ruslan | g | UKR | 2735 | 10 | 1983 |
20 | Dominguez Perez, Leinier | g | CUB | 2734 | 10 | 1983 |
21 | Leko, Peter | g | HUN | 2734 | 10 | 1979 |
22 | Wojtaszek, Radoslaw | g | POL | 2733 | 13 | 1987 |
23 | Jakovenko, Dmitry | g | RUS | 2732 | 9 | 1983 |
24 | Giri, Anish | g | NED | 2730 | 7 | 1994 |
25 | Volokitin, Andrei | g | UKR | 2724 | 9 | 1986 |
26 | Navara, David | g | CZE | 2722 | 14 | 1985 |
27 | Adams, Michael | g | ENG | 2720 | 10 | 1971 |
28 | Tomashevsky, Evgeny | g | RUS | 2720 | 5 | 1987 |
29 | Shirov, Alexei | g | LAT | 2718 | 10 | 1972 |
30 | Andreikin, Dmitry | g | RUS | 2718 | 0 | 1990 |
31 | Bruzon Batista, Lazaro | g | CUB | 2717 | 21 | 1982 |
32 | Malakhov, Vladimir | g | RUS | 2713 | 14 | 1980 |
33 | McShane, Luke J | g | ENG | 2713 | 0 | 1984 |
34 | Riazantsev, Alexander | g | RUS | 2712 | 0 | 1985 |
35 | Cheparinov, Ivan | g | BUL | 2710 | 24 | 1986 |
36 | Areshchenko, Alexander | g | UKR | 2710 | 19 | 1986 |
37 | Jobava, Baadur | g | GEO | 2710 | 10 | 1983 |
38 | Almasi, Zoltan | g | HUN | 2707 | 10 | 1976 |
39 | Short, Nigel D | g | ENG | 2707 | 10 | 1965 |
40 | Polgar, Judit | g | HUN | 2705 | 10 | 1976 |
41 | Vachier-Lagrave, Maxime | g | FRA | 2705 | 10 | 1990 |
42 | Bacrot, Etienne | g | FRA | 2705 | 0 | 1983 |
43 | Korobov, Anton | g | UKR | 2705 | 0 | 1985 |
44 | Naiditsch, Arkadij | g | GER | 2704 | 10 | 1985 |
45 | Nepomniachtchi, Ian | g | RUS | 2704 | 0 | 1990 |
46 | Le, Quang Liem | g | VIE | 2703 | 14 | 1991 |
47 | Akopian, Vladimir | g | ARM | 2703 | 10 | 1971 |
48 | Ding, Liren | g | CHN | 2702 | 14 | 1992 |
49 | Fressinet, Laurent | g | FRA | 2702 | 10 | 1981 |
50 | Vallejo Pons, Francisco | g | ESP | 2700 | 11 | 1982 |
51 | Moiseenko, Alexander | g | UKR | 2700 | 7 | 1980 |

2500 is breakfast to a 2700
No...the ELO is a mathematical model that gives 200 points as an expected score of .75. Thus a 2700 would beat a 2500 most of the times (e.g. 75% win, 25% loss and 0 draws, or 50% win, 50% draw, 0 loss). He is stronger, but you don't have breakfast with players 200 points below you. They take effort to beat.
Of course there's no way a 1400 held his own against a 2500, I don't believe the story posted above.

Of course there's no way a 1400 held his own against a 2500, I don't believe the story posted above.
Well, he did say he lost on time, and the positon was complicated.He probably just misunderstood how badly he was beaten.

2500 is breakfast to a 2700
No...the ELO is a mathematical model that gives 200 points as an expected score of .75. Thus a 2700 would beat a 2500 most of the times (e.g. 75% win, 25% loss and 0 draws, or 50% win, 50% draw, 0 loss). He is stronger, but you don't have breakfast with players 200 points below you. They take effort to beat.
Of course there's no way a 1400 held his own against a 2500, I don't believe the story posted above.
It is possible to get indigestion from breakfast. Indeed, the popularity of pastries and cereals more or less assures digestive problems at least 25% of the time.
Indeed, looking through the latest edition of The Week in Chess, I located perhaps a dozen games between 2500ish players and 2700+ in which the lower rated player did not lose. Most of these were draws, and the lower rated player had White in all but one. There were two wins for the lower rateds, including this upset.
What if the 1300 rated player was rising in points, having only just started playing, and was a chess prodigy similar to Magnus Carlson? Then they could potentially win against the much higher ranking player.

it is not possible for a 1300 to beat a 2700 under normal circumstances. there are stages of development & 1300 is infancy. he should aim at beating 1500 or 1600 then develop like so.

The story actually might have been true. When I was close to 1800 I lost in a 30 minute time control game to a strong Israeli 2600+ GM.
The game was complex, and I got down to Q+R vs. Q+R where the GM told me later that I even had a slight advantage there - it was past move 30.
His R had to guard a pawn on b2, which I was pressuring with my Q.
The GM later told me that my mistake was moving the Q and letting go of that attack, thereby freeing his R. A mating attack on the combined action of his Q and R, to my great surprise, happened in just a few more moves!
I did get an even, slightly better game - but I didn't understand all of the undercurrents of the position, all of the "what can happen if"-s it contained. I didn't see the danger.
1400 isn't 1800, true - but I don't know, The guy may have been playing that game well, and maybe the 2500 got into one of the openings where his playing his rather boring and conventional, didn't put that much effort into that game - we also don't know what the time controls were, and of course we don't know whether by the time the 1400 lost on time, whether his position was still even...

^ Yes almost surely he was positionally busted when his time ran out.
Your game sounds interesting, do you have it?
I would appreciate if you could post it.
In the first round of my first class A tournament that I squeaked into with an 1803 rating, I was paired against a master. In the opening he played a reckless Schliemann Defense, opening his kingside, and before he knew it he had lost his rook in the corner and two pawns for my knight. All this inside of 5 minutes time combined. Then the master sat and thought for 50 (FIFTY) minutes. A half-dozen moves later, my queen was trapped in the corner and I lost.
For a serious answer. About 35 years ago, when I was rated in the 1400s, I had a very good tournament game against a 2500 player (USCF). The game was even, but I lost on time. It was a complex position. It was before computers, so I have never put it up to see how the computer viewed it. So I think it is possible to get a decent game anyway.