A320 Captain reported making an aggressive stop to avoid a collision with a truck approaching at high speed on a surface road.

Narrative

Avoided major collision with a company truck. After pushback and release at gate X at ZZZ; my First Officer (FO) requested a right turn out for taxi clearance due to single engine operations. Ramp Tower cleared us to give way to a B757 turning left from [gate] Y and to turn right; maneuver wide around a B777 pushed back at [gate] Z and proceed on Taxiway 1. I cleared left and forward and my FO cleared right as I released brakes and started a slow right hand turn. I asked my FO to query the Ramp Controller about our clearance because we were expecting Runway XX. The Ramp Controller then cleared us to turn right to Taxiway 2 and Spot 1. As I was making my turn; I noticed movement from my left periphery and looked to see a company semi-trailer proceeding east on the access road at about 30 mph. My nose was already clear of the access road; but my left wingtip was about to swing over the access road and into the path of the oncoming truck. I quickly applied brakes to stop the aircraft. The company truck continued on and came to a stop short of [gate Z] and the B777. My FO alerted Ramp Tower as we taxied to Taxiway 2 that we had almost collided with the truck and they responded that they would look into it. We started the remaining engine; ran the checklist and continued taxiing on Taxiway 3 to Runway XX. I called the Flight Attendants to ensure that everyone was OK and made a quick announcement to the passengers explaining what had happened.