There are two paths to repairing your anvil face: you can grind the surface down to level, or fill in any holes or cracks & then grind back to level. 

If you look carefully at your anvil you will be able to see the dividing line between the hard steel face and the iron body. If the chip doesn\'t extend into the iron you may be able to grind the rest of the face down flush. Its possible to grind the face down to about 1/4"; thick and still have a good and lively anvil.

Consider the number of spots that need repair: to fix a large number of small nicks, you can have machine shop mill off the dings. Don\'t forget to have them grind about a 1/8" radius along the edges so the face won\'t be vulnerable to chipping. If there are a manageable number of dings, you can patch the dings, then have the anvil ground (or grind it yourself!).

Also, try looking at the FAQ at alt.crafts.metalworking, they have a great section on anvil repair.

If you decide to go the "patch it" route, the steps are:

1. select a welding rod
2. pre heat the anvil
3. make your repairs
4. slowly cool the anvil
5. grind the repaired area back to shape, & dress your edges