SECAUCUS, NJ - JUNE 07: MLB commissioner Bud Selig speaks during the MLB First Year Player Draft on June 7, 2010 held in Studio 42 at the MLB Network in Secaucus, New Jersey. (Photo by Mike Stobe/Getty Images)
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The Indians will picking just once today, at pick #15, so I would expect their lone selection to take place around 8:00-8:15 PM
UPDATE:
The Indians selected college OF Tyler Naquin with the 15th overall pick: