Aroldis Chapman -- MLB Investigating Domestic Violence Incident

MLB officials have opened an investigation into Cincinnati Reds pitcher Aroldis Chapman -- after reports surfaced he was involved in a domestic violence incident ... with a gun,.

According to a police report, Chapman's girlfriend told cops the fireballer choked her at their Florida home on October 30th ... and fired 8 GUNSHOTS in the garage.

Cops say Chapman admitted to firing the gun -- but denied the choking allegations.

At the time, Chapman's GF said the incident began after she questioned him over something she found on his cell phone.

Chapman was not charged with a crime over the incident -- with prosecutors saying there was insufficient evidence.

The Reds had been working on trading Chapman to the Dodgers -- but that deal seems to be on hold.