Chickens can sneeze, yes.
It can be from environmental causes (like dust or ammonia levels in the coop or dusty feed) or it can be from a disease.
Chickens don't get colds. It wouldn't be the same as us getting colds. They get respiratory diseases, though. Here is a handy page:
http://www.amerpoultryassn.com/respiratory_disease.htm
Probably the most common chronic respiratory disease is mycoplasma I am guessing from reading lots of posts here on BYC. But things like avian flu and the like would be HIGHLY unlikely.
Here is another link:
http://edis.ifas.ufl.edu/ps044
diagnosis charts at bottom
Generally, I would advocate looking for an environmental reason before getting all worried about a respiratory disease. I just included that info in case you need it. I think there is a blood test for MG now that a vet could administer if he/she deals with chickens. Some respiratory diseases leave the chicken an asymptomatic carrier and can even pass thru the egg to the chick.
For absolutely knowing what the problem is, a necropsy can be done on a chicken by contacting the state vet or county extension agent I believe.
Feed is very dusty at times, as are pine shavings. The chickens themselves put off a great amount of dust, too. If the coop collects too much poo and it isn't kept dry ammonia levels can build up. Check the coop in the morning when you open the door. If you smell ammonia then that could be the problem.