Last night, my wife pulled the ceiling fan light switch chain to turn on the light, and the only thing that happened was the chain extension broke. And now, it appears that the light switch broke too. Is this easy to replace, and would Home Depot or Lowe's have the replacement for a Hunter fan?

Wife is in the dark.

Yes and yes, see:

Ceiling fan pull chain replacement and repair - Ceiling Fans N More (http://www.ceiling-fans-n-more.com/ceiling-fan-pullchain-replacement-and-repair.php)