Chavez, a 15-year veteran, presumably didn't sign for peanuts. After all, his 2012 campaign with the Yankees was his finest since 2007 and the Yankees need a third baseman more today than they have in ... well, it's been quite some time since they've needed a third baseman so badly. With Jeff Keppinger and now (presumably) Chavez off the market, Brian Cashman's options are dwindling.
Meanwhile, Chavez, if he's healthy, should give the Diamondbacks a real boost at third base. Especially if Kirk Gibson platoons the lefty-hitting Chavez and righty-hitting Chris Johnson (which might be a tough decision for Gibson, since Johnson's actually struggled against left-handed pitchers in his relatively brief career).
Update: Actually, Chavez did sign for (relative) peanuts: $3 million, according to Heyman. And people say hometown discounts are dead...