Air taxi pilot reported a NMAC with a helicopter during departure from VNC non-towered airport. No evasive action was taken and the helicopter was not communicating on CTAF.

Narrative

While departing Runway 23 at VNC in Aircraft X; we encountered encroaching traffic [Aircraft Y] on our upwind leg that became a 'traffic-Alert'. The situation unfolded as follows. While in position for take-off with an ATC clearance; we observed a low airborne helicopter [Aircraft Y] about 3;000 feet or so southwest of our position; to the right and more or less parallel to Runway 23. We held in position until the chopper was clearing to the northwest; then at which point we announced on CTAF our take off intentions and started our takeoff roll. At or about our V1 point; the chopper turned southeast and began to head back towards the extended center line of the runway. We saw this happening and the PM (pilot monitoring) made a CTAF call to the chopper about the traffic conflict; (no acknowledge was received). We climbed through their attitude before reaching the end of the runway and then passed clear of the chopper on our upwind (about ¼ mile from the departure end of Runway 23 and along the extended centerline of the runway) clearing the traffic (visibly) by a few hundred of feet both laterally and vertically. This encounter triggered an amber TCAS traffic alert that showed a 100 feet vertical separation and at a lateral distance of a few hundred feet. We continued our departure and flight to ZZZ with no further issues or ramifications from the traffic alter situation.