Well, first... a speaker doesn't "require" wattage really. They all have different levels of efficiency -- that is, how much power it takes to produce a certain amount of sound -- but they will all gladly run on mW levels. Just... maybe not to your satisfaction in terms of volume.
OK, the hair-splitting is out of the way.
Here's a post full of recommendations on small chip-amps:http://www.diyaudio.com/forums/chip-amps/163873-anyone-have-any-experiences-low-wattage-chip-amps.html
I have some little TDAs at home that I haven't played with, but I have built LM1875 and LM3886 designs. Both of those are waaay over your power requirements and supply rail budget though. :-)
If your supply is limited in terms of current (small transformer or battery-powered), you'll need to look into Class D. Unless you're very skilled, that means going with pre-built modules. Those are available all over the place. Check www.parts-express.com
, and Google "class d amp kits".