According to this page: http://www.chess.com/members/member_countries.html
Qatar is best with an average player rating of 1632. Malawi has an average rating of 1810, but they only have 19 members here so I don't know if the sample size is large enough to be considered statistically accurate.
If you are speaking in a more general sense, I'd say Russia is the "best in chess" simply because of the number of fantastic players (including quite a few World Champions) they've produced, followed by some of the other former USSR countries. For example: Estonia (Keres), Latvia (Botvinnik, Tal), Armenia (Petrosian), etc.
Nearlly all of the countries are playing chess in this web site,so which one of them the best in chess???