Christopher Dorner -- Alleged Cop Killer -- Shops for Scuba Gear 2 Days Before Murders. (VIDEO)

Alleged cop killer Christopher Dorner went to a Southern California sporting goods store 2 days before he began his murder spree to purchase scuba equipment ... and TMZ has obtained the surveillance video.

Dorner went to Sports Chalet in Torrance -- a beachside community in the L.A. area -- on February 1st. The video shows Dorner carrying in 2 small, yellow scuba tanks as he walks into the scuba section. Sources tell us ... Dorner got the tanks refilled with oxygen.

The video then shows Dorner leaving the scuba section with the 2 yellow tanks, along with another large, black scuba tank. Dorner then goes to the counter, and then has a friendly conversation with the cashier, at times laughing.

Dorner -- who was a member of a Naval undersea warfare unit -- pays cash for the items and then leaves.

What's really interesting ... Dorner reportedly tried stealing a boat in San Diego on February 6th ... where scuba gear might come in handy. The plan was thwarted when the prop got tangled in a rope.