Occasional Starting Problem (sporadic NO crank... dealership can't find problem)

I have a 2009 Aveo purchased new and currently prox. 100K miles. As far back as the first year of ownership, I have had sporadic starting problem. Car will refuse to start, no cranking, no nothing. May repeat attempt numerous times. Then it will suddenly kick right over. When running, it runs fantastic. The problem may not occur again for several months or it could happen the next day. No pattern whatsoever. I originally had it checked by the Chevy dealer and they couldn't replicate the problem and got no bad readings. Later I had my own mechanic check the starter, and found nothing and couldn't replicate the problem. I'm reluctant to pay a mechanic to blindly troubleshoot and come up blank. I replaced battery a couple months ago, problem still exists, no better, no worse. Ideas?????

Swap in a new starter relay - very inexpensive and easy thing to try.