Ahaha, I know this one. Dean Chance, 1967.
The only reason that I knew it right away though is because I just happened to watch For The Love of the Game last night. I hadn't seen it before so after watching it, I jump on the net and was looking up perfect games and near misses and happened to see that one.
Next question (again, could be tricky if you don't pay attn)
How many numbers do the Twins have retired? (bonus cyber-points for listing the numbers and the names associated with them)