The connotation of the term "rearing" is typically a parent-child situation, and it implies that care is provided for the child by the parent (including protection, provision, and education). While "rearing" can be used in an animal situation, it would apply more toward the animal mother rearing her litter or offspring.
It would be assumed from the fact that this is chicken farming, that you are talking about humans taking care of the chickens. In this case, the most acceptable word would be "raising." Many critics believe the term raising chickens is most appropriate for a farm with a smaller number of chickens.
Example: My neighbor raises chickens and sells the eggs at the farmer's market on Wednesdays.
If you are talking about mass-production chicken farms (like Tyson or Perdue), the term "raising" is still used, but applied liberally, at best. Have you heard the term CAFO (Concentrated Animal Feeding Operations)? CAFO critics would assert that the term "raising" in this case implies a little bit too much personal human involvement. A more appropriate term to describe these kinds of chicken farms would be chicken production and distribution. More often than not, such farms are not egg farms, but rather, chickens are produced for their meat. Such critics believe it is a little too generous to suggest the farm "raises" the chickens, as they are largely penned up for the duration of their short lives, fed by machines, and slaughtered in an assembly-line fashion.