Steel frame tubes generally have decently thick walls. You'd need an awful lot of corrosion in the chipped spots to weaken it in any significant manner, and it would have to be a pretty large area of the metal that had corroded, really. More of a worry would be it leading to getting moisture under the paint in the surrounding area, but a decent bike usually has a paint job that's tougher than that as well.
If it's a fresh chip, just touch it up with a closely matched nail polish / automobile touch-up paint, or if it's a hard to match colour, maybe some clear nail polish just to protect the metal.
On my 30+ year old bikes they have usually come to me with lots of chips and scratches that had rusted in the first place and I've removed the oxidization on the metal with WD-40 and/or vinegar. Not at the same time, naturally. I stripped the paint from the frame of an old Grand Prix that was more rust than it's original finish and underneath was plenty of good strong steel. I wouldn't worry about a chip too much.
I typically use some car wax at the beginning of the season to protect the exposed metal and leave it as is, but my bikes only really see rain when they're being ridden in it. Maybe if you park it outdoors in all seasons you might want to put something more resilient than wax over it.
All in all - don't be afraid of some chips and scratches, they add character to the bike.
