Save the limestone chip, if possible. Chips in large pieces or a single piece can be reattached, while shattered chips require replacement.
Clean the damaged area with hot water, liquid dish soap and a stiff-bristled brush. Remove any dirt clinging to the stone or around the damaged area. Clean the chip using the same method, but scrub lightly so you don't crack it further.
Apply a limestone patching compound, available at hardware stores, to the chipped area. These compounds require mixing to work properly, so follow the package instructions exactly. Use a patching compound in the same color as your limestone so that the repair is less visible.
Press the chip into the compound, lining it up with the surrounding limestone. Scrape the surface seams with a putty knife to remove the excess compound and smooth it into the seams. If the chip isn't available, smooth a coat of color-matched compound over the area with a putty knife. The epoxy provides adequate coverage for small or shallow chips.
Fill cracks in limestone blocks with the epoxy, forcing it into the crack with the putty knife. Smooth the surface of the repair with the knife, feathering the edges onto the surrounding unbroken limestone so that the repair is blended into the stone.
Allow the compound to dry for the amount of time stated on the label, usually 24 hours. Sand over the compound lightly to smooth any rough or protruding areas, if necessary.