ouachita solved chess.
Is it possible to solve chess?
In theory yes, of course. The game is finite and once we have working quantum computers there's a real chance that it could be solved. It won't happen in my lifetime, but yes, eventually.

Just get roadrunner (world's fastest computer) running for a couple decades, and we might get 15 moves in. :P

The number of positions is not nearly as high as everyone thinks if you consider the illegal and drawn positions.
Pawns never can be on the first and eighth ranks, both kings cannot be in check, you cannot triple check a king, both kings must be on the board, in the endgame you cannot have just a bishop or knight against a lone king as it is a draw.
This drastically reduces the number of positions available.
Now tablebases have been created up to six pieces so those positions are already known.
Now the number of remaining positions still remains large, but not at the numbers people suggest at 10^100+. This should be within the realm of quantum computing.

I think in theory it could already be solved by the software we have now. The only problem would be the length of time you'd have to leave the computer running for. I'm guessing billions and billions of years
Also, I've thought of a problem with this. Currently engines operate by assigning a value to a position, e.g +0.25 means white had a slight advantage. If, one day in the distanst future, a computer was to 'solve' chess, surely it would encounter this issue: All positions are now scored as either +Infinity, 0 or -Infinity. So, for example, why is 1.e4 now any better then 1.h4? After all, they both result in positions the computer knows are drawn, and are thus scored equally as 0. So wouldn't the computer make bad moves at the start of the game, until it reached a point where the position was *almost* lost but holdable with perfect play, and then produce that perfect play to draw the game? In other words, it would never lose, but I'm not so sure it would win either!

A three (including kings and pawns) piece endgame would contain ~60,000 positions.
A six (including kings) piece endgame contains 17,823,400,766 positions.
Now you will eventually have to reach a 14 piece endgames and the number of positions will become extremely large, but it could be on the order 100,000,000,000,000,000,000,000,000 or 10^26 as adding a piece increases the number of positions by two decimal places. Now if you include pawns the positions will increase and then the promotions to pieces you could conceiveivly have even higher piece endings. This is still less than 10^100+

Now tablebases have been created up to six pieces so those positions are already known.
Indeed, and I'm gonna buy that 1.5 T external hard drive at Costco so that I can store them. Soon (five years or so), the seven piece tablebases will be available, and by then 2 T of storage will be common enough on cell phones, but the tablebases will require far more storage than available on most desktops.
AS for your other assertions, you oughta look at the research done by François Labelle who does "consider the illegal and drawn positions": http://wismuth.com/chess/chess.html.

Sorry to reply to my own point, but this has really got me thinking! I can think of two possible solutions to the problem I outlined, about the computer not recognising one 'drawn' position as preferable to another:
1) Rank drawn positions based on the number of possible lines that result from them leading to a won position, compared to the number leading to a lost position.
2) A dual approach of combining 'solved' chess with a current Fritz-like engine. The engine would analyse and make moves, just like today, except all moves it tries to make would be pre-checked against a database of all the lost positions, just to make sure the machine cannot lose.
Personally I prefer the second idea because the first idea would run into the problem of the computer swapping off loads of pieces aimlessly - "If I take his knight with my knight, almost all replies lead to a won position for me, except one (the obvious recapture), so this move must give me a better chance of getting a won position than any other".
So this dual approach is the best I can think of so far, but I'm all ears for better suggestions.
The number of positions is in the neighbourhood of the number of atoms in the universe. How can you store all that information? Is it even physically possible?
Actually far higher.
10^120 chess (likely higher)
10^83 atoms (likely lower)
OTOH, Rybka 4.0 is close to being capable of never losing with the White pieces.
While your estimations of the numbers may be correct, you should note that not every game tree needs to be exhaustively examined: an algorithm may be developed which can find the best move from any position (kind of like the fact that we are able to multiply 2-digit or 3-digit numbers using a long multiplication method with the definite certainty that we will be right, despite not having a tabulated database with all of the answers).
As for Rybka 4.0, it never (figuratively) loses as White, very rarely draws as White, very rarely loses as Black and rarely draws as Black. As White, it's results are around 95% (90% wins, 10% draws); and about 85% as Black (75% wins, 20% draws, 5% losses). And that's against the best computers in the world, meaning that it dominates with an exceptionally strong fist. But I don't see how that relates to the question?
Computer Go players can barely keep up with beginner to moderate level chess players. It is simply much too complex.
A computer beat a Go master for the first time last year (I think it was).
Found it: "In 2008, thanks to an efficient message-passing parallelization, MoGo won one game (out of three) against Catalin Taranu, 5th Dan Pro, in 9x9 with standard time settings (30 minutes per side)."
http://en.wikipedia.org/wiki/Computer_Go#Recent_results

Some hyperintelligent, pan-dimensional beings already built a program to solve chess. They found that the answer is 42.

I read this somewhere, and apparently the "perfect" chess computer would have an elo rating of approximately 16,000. Since the highest current rating any man/machine has now (the year 2010) is about 3400 from Rybka 4.0, we still have a long way to go.
As there is 6 different pieces per side, each square has 13 different options
as there 64 squares
13^64=1.96x10^71 possible positions you could make with chess pieces and a chess board.
there is about 10^17 per cm^3
So there is about 1.96x10^54 cm^3 amount of atoms If number of atoms equal the number possible chess positions
And the earths volume is 1.1x10^24 cm^3
So it would take 1.78x10^30 earths
There are around 10^80 atoms so their is more atoms than possible chess positions

As there is 6 different pieces per side, each square has 13 different options
as there 64 squares
13^64=1.96x10^71 possible positions you could make with chess pieces and a chess board.
there is about 10^17 per cm^3
So there is about 1.96x10^54 cm^3 amount of atoms If number of atoms equal the number possible chess positions
And the earths volume is 1.1x10^24 cm^3
So it would take 1.78x10^30 earths
There are around 10^80 atoms so their is more atoms than possible chess positions
You're missing several key elements, not least that chess is played through sequences of moves not merely static positions.
Measuring the atoms in the universe must assume a finite universe. I don't understand such claims. Best to stick with an infinite universe, it gets the pesky, cartoonish cosmological gods out of the way