Inspired by Fear, Loathing, and Gumbo On the Campaign Trail '72, an excellent timeline by Drew...
What if Barry Goldwater, Jr., then a Republican congressman from California, ran for Governor of California in OTL 1974? He would be up against Jerry Brown, so if he defeated him, that would be a pretty big butterfly right there.
I imagine he could win - if he could just play off Ronald Reagan's popularity as governor, and get the retiring incumbent to campaign for him, it could be very easy, though I can't see a Goldwater '74 landslide.
So how would he do as Governor? What would happen to Jerry Brown? I don't think he would run for the GOP nomination in 1976 if Reagan ran. So, assuming he's re-elected in 1978 and Jimmy Carter is elected POTUS in 1976, would he run for president in 1980? And what if he doesn't run, or loses in the GOP primaries?