I had never really thought about grocery store chickens until I started raising my own.  The chickens you buy at the grocery store are universally the Cornish X (Cornish Cross) breed.  This breed was developed by crossing the Cornish and Plymouth Rock breeds, with the goal of a chicken that will put on a lot of muscle very quickly.  In fact, most of the whole chickens you find at the store are between six and nine weeks old.

It is possible to buy industrial strains of Cornish X chicks to raise at home, and many people do.  April, who writes the Coal Creek Farm blog, recently went through the slaughter process with her Cornish X chickens.  She also blogged periodically about them as she was raising them - they ate a phenomenal amount of feed!  Although she purchased 20 chicks, she only ended up with 17 edible carcasses.  Two of the chicks died early on, and a third was sick at butchering time.

This raises another problem with the Cornish X breed.  Because they put on weight so quickly, they have to be slaughtered young, before they develop heart and joint problems.  Put simply, their own internal organs simply can't keep up with their growth rate.  A Cornish X which is not slaughtered in time may well suffocate under its own weight, or be unable to get up on its feet to feed and drink.

Some people have reported limited success with keeping Cornish X chickens as pets.  The key is to severely restrict their food intake.  Blogger Heather Houlahan at Raised By Wolves bought four Cornish X chicks as an experiment (she named them all Cartman).  Even though she blocked their access to feed for 12 hours a day, they still grew far faster than the other chicks she raised. 

An interesting side note: "cornish game hen" is simply a baby Cornish X chicken, slaughtered at about four weeks of age.

The industrial breeds of Cornish X were bread up from the Cornish breed of chicken.  The Cornish is a perfectly normal breed of chicken, with a normal lifespan, although it has a propensity to grow rather quickly.  This trait has been strongly exaggerated in the various Cornish X breeds being raised by industrial chicken processors.
 
Each corporation keeps two lines of Cornish X: one male, and one female line.  All of the females are culled from the male line, and vice versa.  In order to produce chicks, members of the male line are bred with the female line.  Each line is carefully kept separate, and their hereditary backgrounds are "closely-guarded and coddled corporate assets." 

Because the chickens won't breed true, chicken producers have to keep going back to the parent line to buy chicks.  This has the interesting side effect of locking in the money for the company which holds the parent lines.  It's similar to the genetically engineered strains of wheat and corn sold by big agribusiness corporations, which are sterile so that farmers have to purchase seed every year.