<chuckle> I hear you on the $400 part, me too. The problem with solar is that you have to have a bank of batteries large enough to carry you through the night and possibly for several days to a week or so depending on possible overcast/cloudy weather. Then there is a charge controller to add to the equation, monitoring of electrolyte levels and specific gravities, possibly an inverter, etc.,etc.,. It's much easier to walk into the coop and just flip a switch and swap a light bulb out every now and then.
Plus....you can run fans, lights, heat lamps (brooders), radios, etc.,.
100' shouldn't result in much of a voltage drop and should run small motors ok. 12/2 wire should do the job. You can use direct burial wire buried in the ground or either slide it in conduit/pvc for physical protection.
Mount your receptacles up out of the reach of your chickens.
Hook up a ground-fault-interupt (GFI) either at the breaker box or at the outlet box (preferably at the breaker box) and you should be good to go. GFI's can be purchases to fit inside your breaker box or either as an actual plug receptacle (like those plugs in hotel rooms around the lavatories that you sometimes have to press a button on to make them work).
The following was priced at lowes.com:
100' of 12/2uf (underground) $79.00
20amp Square-D GFI Breaker 38.00 (a GFCI receptacle would be around $15.00 if you go that route)
Misc. wire nuts, receptacles,... 20.00
Rough guesstimate............. $137.00 plus tax and any labor (burying wire?)
Best wishes,
Ed
Voltage drop per 100' of (paired) wire: