A Cessna 310 pilot reported oil streaming from the left engine while inflight; resulting in an engine shutdown; and a return to the departure airport.

Narrative

I was participating in an animal rescue departing from ZZZ and picking up the animal in ZZZ1. The flight in my Cessna 310D from ZZZ to ZZZ1 was uneventful with landing in ZZZ1 about XA:30. After departing ZZZ1 with the single animal the intended drop off was to be ZZZ2. On departure from ZZZ1 I contacted ZZZ Center for VFR flight following to ZZZ2 and continued climb to 9500 MSL my intended cruise altitude. At about XB:19 I notice oil streaming from the left engine and also noticed that the oil pressure gauge indicated zero oil pressure on that engine. I confirmed that the right engine was operating normally and decided to shut down the left engine which was accomplished according to the Cessna POH checklist.Just before this ZZZ Center transferred me to ZZZ1 Center and I informed them of the situation. Because I was near ZZZ3 I told Center that I would be diverting to ZZZ3. I reconsidered this decision because ZZZ3 Airport has no services and I am based at ZZZ. The aircraft was under control and was maintaining altitude. I then [requested priority handling] with Center and decided to proceed to ZZZ. ZZZ Center handed me off to ZZZ Approach and then to ZZZ Tower. Landing was uneventful and the aircraft was towed to my hangar. Upon inspection by my mechanic it was determined that the left engine had experienced a significant oil leak caused by a oil sump drain plug that had become dislodged. This caused the loss of oil pressure necessitating the engine shut down. My mechanic examined the engine and it was determined that there was no damage to the engine or airframe.I would like to commend each ATC facility that managed my [incident] professionally and gave me all the help that I needed for a safe conclusion to my flight.