1968 Z/28 VIN Number
 

I googled and did a search on this Forum for this VIN. # 124378N384828 and came up with nothing. Does that mean I should stay away from this car?

Not at all. Just means it hasn't been discussed on this site.

There are many undiscovered cars out there.

No reason to not at least check it out. I am not endorsing the car, just saying that any first gen needs checked out thoroughly before purchase.