Hall of Fame Brain Teaser

When I'm bored or trying to fall asleep, I like coming up with baseball brain teasers. Here's one that I haven't figured out yet:

Name a current Hall of Famer who never played on a team with another Hall of Famer.

I thought I had this figured out. I thought that George Brett was an answer, but then I remembered that Gaylord Perry was on the Royals in 1983, and Harmon Killebrew in 1975.

Another potential answer was Tony Gwynn, but he played with Roberto Alomar back in the late 1980s. Or how about the newly inducted Barry Larkin? Well, Tony Perez was on the 1986 Cincinnati squad, the year Larkin was called up.

It's sort of like a reverse Six Degrees of Kevin Bacon, and harder than you think. I'll post a list of the permutations later in the week, but in the meantime, post your responses as comments on this post.