I came home from a trip a month ago and found a gravel road in front of my house. The township I live in decided to enhance the rural character of the area by converting the road from blacktop to gravel. So far I've picked up two very small chips to the paint. I have to drive about a half a mile on the road in either direction. As slow as I go the tires seem to pick up chips. The diameter of the holes is no more than a sixteenth of an inch but they are deep. I don't see bare metal. There appears to be a layer of body putty or something under the paint.
Has any one had experience repairing chips like these. Should I just use many coats of touch-up until the paint fills the void? Should I finish with clear coat?

Thanks for any help,
Johnnie