Here's a handy tool to test it: http://browsercookielimits.iain.guru/
It reveals quite a lot about the internal details regarding cookies. Click "Run Tests for Current Browser" for the results (it only takes a moment).
For example, I ran all tests for Google Chrome 10.0.648.134 beta:
22:23:46.639: Starting
22:23:47.345: Count: Max Cookie count with Character Length 3 and character "1": 180
22:23:50.131: Size: Max Cookie Character Length using character "1": 4096
22:23:52.347: Count: Max Cookie count with Character Length 4096 and character "1": 180
22:23:54.517: Size: Max Cookie Character Length using character "ÿ": 2049
22:23:57.450: Count: Max Cookie count with Character Length 2049 and character "ÿ": 180
22:23:59.41: Count: Max Cookie count with Character Length 100 and character "1": 180
22:24:0.535: Count: Max Cookie count with Character Length 10 and character "1": 180
22:24:2.88: Count: Max Cookie count with Character Length 5 and character "1": 180
22:24:2.886: Guessing Max Cookie Count Per Domain: 180
22:24:2.887: Guessing Max Cookie Size Per Cookie: 4096 bytes
22:24:2.887: Guessing Max Cookie Size Per Domain: NA
This answer is pretty old, but I just checked results for the latest Chrome version, and they're essentially the same.
Edit: updated the answers for Chrome 54.0.2840.98 (64-bit).