Scot that anvil requires no "fixing" whatsoever. There is nothing wrong with it and nevermind the chips, just work around them. If you simply must have a good clean edge to work with then investigate the heel, that edge is usually chip free. Working cold iron is what put those chips there so remember, strike while the iron is hot!
Do NOT feel you must "fix" anything such as weld or grind on it. Just use it as is.
Congrats, you scored a nice anvil.