There's so much debate about electric fencing, dogs, etc... so there's not much for me to add, however I would like to share a few thoughts.
*First of all, no one has mentioned YOU, YOUR FAMILY, YOUR HOUSE, AND YOUR CARS: Be careful. They will rip off car doors, house doors, windows, etc. Please be careful to properly store your trash, don't leave food in the cars, or near house doors, and keep your wits about you while outside. Hopefully they are just moving through your area naturally, not because they've learned humans mean food.
*Bears are VERY smart and can smell things for miles. I think that if it is attracted to your property and is hungry enough it WILL get in to where ever it smells good to them.
Some things I read:
"Garbage should be stored in airtight containers and placed in a secure area. Containers should not be stored in a wooden shed or against garage or basement doors and should be washed with a disinfectant at least once a week to remove odors. "
***Big note on the storage of food, not trash, but food. And I don't mean for this to be a plug but... my family business makes approved bear proof food containers, not those shotty "bear proof" trash cans that only keep humans out. They are meant for human food to be kept safe while in the back country. Many places actually require them. They are tested by the US Forestry service and we have a very high success rate. They would fit a 50 lb bag of feed easily. A bear can toss it around all it wants and it would be highly unlikely that it would even get a kernel. Check it out and if you're interested call us. Ask for myself, Jessica, or my Dad, Jeff. We'll take care of ya!
http://www.bear-aware.com/
"The outside feeding of dogs and cats should be done during daylight hours and all uneaten food and scraps, as well as food bowls, should be removed immediately after feeding."
My quick thought about electric fences - Although I have limited experience with electric fencing, I do know that the hot wire we use for our horses doesn't deliver a constant shock, it's more rhythmic, zap.... zap.... zap... but strong ones. I do not know if all electric fences operate like this... Here's my thought... Our horses are smart enough to sense the 2-3 second pause in the surge and they test the fences at those moments. I know bears are just as smart if not smarter than horses, so I think that something with a constant surge would serve a bit better. If they figure out that the fence is not electrified even for a moment, it could charge the fence and bam, they're in.
With all this said... In my opinion... Try your best to keep your chickens and their food as well contained as possible, he may come after their feed just as much as the chickens themselves. Keep your place, chickens and people, as sanitary and clean as possible. There's a CHANCE that you're property can be so clean and "boring" to a bear that it wouldn't bother nosing around. Chose your fencing methods to the best of your ability.
Good luck
and be safe!