From an e-mail that just came through from the Romney campaign:
We're getting ready to share some exciting news. Sometime between now and the Republican convention, Mitt will be announcing his choice for VP.
Know what's even more exciting? Every week until the VP announcement is made, one lucky supporter will win the chance to meet Mitt and his choice for VP.
UPDATE: I noticed shortly after posting (as was pointed out in the comments) that the wording of the e-mail is ambiguous enough to suggest that contestants will actually win the opportunity to meet the running mate in coming weeks, not actually meet them during that timeframe (which actually makes more sense in terms of preventing leaks).
And Drudge is now reporting Condi Rice as the surprise candidate "near the top of the list." As of yet, however, there is no sourcing, even on background.