Obviously your opponent was just a jalous guy, but there's a lot of. I'm often insulted and accuse of cheating (I never cheat). Those opponents are just jalous guys who don't accept losing, so never answer them, they will never tell you they're wrong.
Cheating Accusation
Block him and move on - looking at his profile it shows that he does this on a regular basis.
One should only report (http://support.chess.com/Tickets/Submit/RenderForm/20) if:
- Anything lewd, sexually inappropriate, or pornographic - this includes text, images, links, etc
- Anything offensive, threatening, or intentionally discriminatory to any race, gender, sexual orientation, etc
- Anything slanderous, threatening, or malicious toward any user
- Anything "spam" (links to commercial websites where not approved, etc)
But if a solution is blocking or disabling live chat, that is preferred. Reporting is for generally repeat offenders.

No doubt about it .. sometimes my opponent just seems to move so accurately through the whole game .. perhaps with a little (seemingly unnatural and robot-like) pause between moves .. that by the end of the game something just doesnt seem right - especially if they are 200 points below you! Its very frustrating :(
Are they cheating? Maybe .. I mean it would be simple to quickly put the current game into your phone .. would take 20 seconds maybe .. So maybe not used in 2 mins but highly possible for a 5-10 min game ..
But at the end of the day what does it matter.. ? Chess can be such a cruel game and you win and lose some. Just keep going and try to improve its all you can do really ;) and try to enjoy it lol!!
Those cheating accusations are as much bad style as publishing them and the name of the accusator on the forum is.

i always get accused of cheating
Wow, what computer do you use to cheat?
Please tell me! I can play it and finally beat a computer a computer at chess!!!

Biggest commpliment you can get dude,just say to people like this "Good job dude,you just beat Houdini and you suck, you must be using better engine!"

Serious question: At what rating, would a person be skilled enough to be able to suspect another of cheating. I ask this because at my level I wouldn't have a clue if someone was cheating or just better than me. Of course, the good new is I'll never suffer the annoyance of being accused of it.

Well,haught, you really cant prove for sure,only suspect.They could turn on engine for a couple of moves if they were smartband you wouldnt know. Chess.com uses software to determine if people are cheating.Dont worry about it ,its only a game unless your making money at it.It can only make you better anyway
For the first time I've been accused of using an engine (in a blitz game at that). I'm not quite sure how my opponent reached that conclusion, but he was quite obnoxious about it in the chat. I eventually did bite back. I kind of think I may have sunk to his level by the end. Normally, I can ignore insults but something about accussing me of using an engine really riled me up. Well the chat is below and the game with comp analysis (to show that it was very flawed). I'm curious what others do in these situations. I guess I've found a pet peeve of mine, I'm wondering if other chess players share it. Call me an idiot, and I'm ok. Accuse me of cheating, and I'm close to spouting obscenities. I've generally had pleasant experiences with chat so I'd rather not start turning off do to the odd undesirable.
EskimoPete: you're not playing like an 1178 rating, what chess program are you using to cheat?
EskimoPete: is it worth cheating to win at online chess? really? how said is your life that you cheat at online chess
mjh1991: I am playing at about this level. I don't cheat. I wouldn't be rated like this if I didn't blunder a lot.
EskimoPete: no, i'm asking what chess program you're using to cheat
EskimoPete: and i'm making fun of you for cheating at online chess
mjh1991: I'm not cheating. Learn to take a loss like a man.
EskimoPete: not what i'm asking, i'm asking what chess program
EskimoPete: i'm very sorry for you btw