Chessie is a free chess game that has none of the usual complexities, making it as simple and lightweight as possible.
There's a cost to taking this approach, of course, and graphics is one of the first. There are no gorgeous lifelike 3D chess pieces here; you play with basic icons. These can't be dragged and dropped to move them (instead you click on a piece, then where you want it to be moved). And there are no extras, like playing hints or network multiplayer options.
But on the other hand, you do get multiple difficulty levels. If you run out of time then you can save a particular game to continue it later. Or, if you'd like to practice your skills anywhere, then all you have to do is copy the program's executable file (a tiny 1.58MB) to a USB flash drive. Plug this in to any convenient PC (Windows 2000 or later) and your portable chess opponent will be ready to do battle.
None of this will be enough for grandmasters, then. But if you're a chess novice, looking for a lightweight and portable chess opponent, then Chessie may appeal: it's definitely worth a try.