Hi Silas,
as per Olly's suggestion, "Tile'n'Tub" is an excellent product, it comes in 2 containers & you simply mix it & apply it to your bath tub & it comes up looking a treat... you just have to follow the instructions on the pack & it is dead easy (simply do 2 coats)...
I did one bath tub 1.5yrs ago in an IP & saw it the other day & still looks good (mind you I applied it to re-colour the bath tub from blue to white)... it was easy to do, clean tub & sand it back with a wet sandpaper... I'd personally use it again...
In terms of your chips, I can't see a reason why this products wouldn't work, may need to sand it back a little more around the chips to hide them, but worth a try...
Cheers,
MannyB.