J Lo surprised the Chicago crowd at the National Sports Collectors Convention when 10 minutes into A-Rod's signing session ... she quietly walked out from behind a curtain and sat next to him. Witnesses say there was zero fanfare or announcement ... which, let's face it, is NOT typical when J Lo enters a room.
We're told Jennifer just beamed at Alex while he signed items for fans -- minimum $150 a pop -- and she frequently stood up to snap pics of him. Y'know it's love when she's happy to watch you work ... and work is signing your name over and over and over again.
Interestingly, we're told J Lo didn't sign anything -- and that's where we think everyone struck out.
An autographed, game used J-Rod ball's gotta be a moneymaker!