It's realistically doable in your basement. It just requires a lot of startup capital relative to a computer. I've long wanted to play around with garage genetics, and even on my graduate student salary, i've put away enough that i could afford pipet sets, thermocyclers, enzymes, etc. I just dont have the garage. Or enough room in my apt. to put the stuff. Or a really good idea worth spending all this money on. Or a purchasing account with a respectable scientific supplier.

Chickens do NOT have any need for a speciation (leap, in your terms). In fact, they have the exact opposite. We put significant selective pressure on chickens to breed fast, grow large, and otherwise sit around not escaping (basically, to do what chickens do best). Any 'mutant' chickens would fail to be 'better' in the sense of 'having more offspring' than a typical chicken, unless they were better at breeding, being fat, or being docile. Any of those would still be chickens.