BE-55 pilot reported an issue with one of the propellers and shut down one of the two engines while in cruise. The pilot diverted to an airport along the route of flight and landed safely.

Narrative

I was cruising at eight thousand five hundred ft. with all systems operating normally. I had been airborne approximately thirty five minutes after and uneventful departure and climb out from ZZZ. At an instant there was a significant change in the sound from the engines/propellers. The sound was constant but a completely different frequency than normal. All of the engine instruments appeared normal and all indicators from both engines continued to match. However; due to the change in sound it was clear something wasn't right. I could not tell which engine was the problem; so I began to trouble shoot. Since I suspected the issue was likely the propellers; I began with adjusting the propeller controls. I first adjusted the left propeller control and it seemed to operate normally. Just as I was reaching for the right propeller control the entire airplane began to vibrate violently. I immediately feathered the right propeller. It continued to rotate; however the vibration remained; albeit less violently. I cut off the mixture to the right engine and the propeller stopped rotating. Also; the vibration ceased. At the first change in sound I made a left turn to my departure airport. I was under VFR flight following the entirety of the flight. I was talking to ZZZ Approach when I first had the issue and was subsequently switched to ZZZ1 Approach. Upon checkin with ZZZ1 I [requested priority handling] and changed my destination to ZZZ1. Since I was getting very good power from the left engine; I felt I could make it closer to home. I subsequently lost communications with ATC using my number one radio and suspected I might be developing an electrical problem. So; I made a right turn toward ZZZ2; where I made an uneventful landing. I initially suspected that the propeller had failed. That was my initial thought while airborne and I held onto that idea until I took the time to further consider the condition of the propeller. With big chunks of metal missing from one of the blades and the other blade and all other parts of the airplane completely untouched; I suspect I may have made contact with a drone. This is pure speculation as I did not see one. However; from take-off and well into cruise; the airplane was flawless and the air was smooth. Also; the change in noise from the engine/propellers was instant. From the change in sound coming from the engine to the violent vibration was less than thirty seconds. After securing the engine; and setting up the fuel controls for cross feeding; I was very comfortable flying the airplane single engine. Maybe a little too comfortable. If I were to go through this again I would have diverted sooner. I believe my high flight time and having experienced more dire situations while flying in the military may have led to me being a little too comfortable with being single engine in a twin. However; once the divert decision was made; my training allowed me to successfully land the airplane without further complications. Once [priority was requested]; anything; such as picking an airport to land because of the availability of maintenance on the field should not enter into the decision matrix. Landing at the nearest suitable field is just that. Nothing more and nothing less.