See if these help you.
You will need nail polish remover to clean the granite surface, straight razor blades, thick super glue (gel), and if you have a darker Granite Countertop you might want to have dark Sharpie marker. Start cleaning your chipped area with nail polish remover. Let the Granite air dry. Tape off the area surrounding the chip and apply just enough glue to fill the chip and rise just slightly above the surface of the stone. Filling the glue up to within flush of the surface of the tape should be sufficient. Once the super glue has completely dried and the tape removed, use a straight razor blade to remove the excess Super glue by “fanning” the excess material away. Wait and allow the glue to cure before cutting with the razor. The time it takes for the glue to cure depends on how deep the chip was, the humidity in the home, etc.(This next step only applies if you have darker Granite) Once desired results are achieved, you may wish to use a colored permanent marker such as a black Sharpie to color the super glue. A Sharpie is permanent and dries quickly. For lighter colored stones, this may not be necessary.
The repair options out there don't seam to be very easy or long lasting. I'd call the granite yard and see if they could send someone out to round off or sand.
You can fill in chipped edges with Bondo, smooth out and try to paint with oil based paint to match your stone.
If the chip is jagged and you are concerned about safety, my suggestion as a non-construction, especially granite, person, get the lighest sandpaper available to you and very lightly just sand, maybe in only one direction. Best wishes.
"lightest" meaning finest, smoothest