First, check for vacuum leaks.
If you find none, remove and clean the TB (throttle body) throttle plates and Idle Air Control (IAC) motor pintle.
I might also replace the fuel pump and filter if you think both are original. There are many things in a Corvette's life that need changing before they go bad.
Check the oxygen sensors, TPS switch and the EGR solenoid, too. If your car starts OKAY in the morning then, stalls right afterwards, I'd highly suspect the fuel pump.
Still, the most common reason for stalling, not accompanied by hard start and or stall after starting is lack of a tune-up and throttle body cleaning.
After you remove the throttle body unit, take some Valvoline Synthetic Throttle Body Cleaner, spray it on a rag, open the throttle and while open, push the rag in and around the throttle plates.
I also like to use an old toothbrush to clean the inner housing and IAC motor real good.
You will see the dirt and carbon build-up. I'm almost 100% positive this will solve your problem. Do this once a year. It really mellows your base idle and improves throttle response, too.
PS- Don't worry about spraying the TB cleaner directly into the throttle unit. It won't damage the Throttle Position Switch (TPS).
Art
Srarts, runs great... won't idle
Linear Mode
