The rear end of my 1988 Camaro makes a chirping sound while I am driving. When I brake the sound stops. I have no idea what could be causing it and would love some input on what I should check

 

Its probably just your brakes dragging a little. I guess the 88 does have discs on the back doesn't it? I have had many cars squeak while driving and it stops as soon as I touch the brake because it is tightening the brakes against the disc.

 

His 88 was most likely drums, although discs were an option. Pull the drums off, hose everything down with brake cleaner really well, regrease the brake shoes where they contact the backing plate, make sure all other hardware is still good (this is when you check to see if your adjuster still moves). If everything is good, reassemble and adjust your brakes. Your squeak should go away.