Captain reported while performing pre-flight inspection removing the nose wheel chock resulting in the aircraft rolling and striking a fuel truck before the crew was able to regain control of the aircraft.

Narrative

We were on the process of shutting down when we received a call from scheduling informing; we needed to accomplish another leg. It was agreed to take the aircraft to; ZZZ to avoid the ZZZ1 TFR on the following day; and to reposition closer to our next destination. The APU remained on; and some exterior post-flight became another exterior pre-flight. We waited on lav service and fuel; as well as service. Lav was serviced and service cleaned the aircraft. I recall looking at the brake handle and seeing it set. As the lav was done; I requested the lineman servicing the lav to uncheck the main gears; as we were preparing to leave. The fuel truck arrived; and a fuel load was provided. Upon completion of fuel; I checked with my colleague; and the onboard fuel was good. I locked the fuel door and proceeded to complete my final walk-around. All was going according to plan; until I removed the nose-gear chock. Normally I ask a line personnel to unchock; however; the ramp was congested; there was a TFR; and a government official was about to land. We had a departure time of XA:00L. While none of the procedures were accomplished in a rush; we felt the need to depart as close to on time as possible. Upon removing the nose-gear chock; I stepped away from the aircraft to drop the chocks and the carpet. When I looked back; I noticed the aircraft starting to roll. I ran towards the aircraft and was able to climb onboard. I noticed my colleague attempting to brake the aircraft. I heard the hydraulic aux pump on; and my colleague trying to stop the aircraft. I went for the emergency brake pull handle; however; my colleague got to the handle first. Regretfully; the aircraft rolled 2 to 4 feet before it came to a stop. We noticed that the right wingtip clipped the fuel truck; still parked; and the driver preparing to leave. The wingtip hit the truck; causing minor damage to wing; and no apparent damage to the truck. I was convinced the brakes were set; for I do not recall removing the brakes. It is normally the last thing I do prior to securing the aircraft. It appears the brakes either had low pressure; or were not completely set (half-way set).It is very important to pay attention to detail and to ensure everything is in place when operating or about to operate an aircraft. While we were not rushing at all; there was some pressure to accomplish all tasks and depart as close to on time as possible. A lesson has been learned with this mishap. It is important to double check or triple check the brakes are set (including dual confirmation); and no vehicles or personnel are near the aircraft prior to removing the chocks. Moving forward; I ensure that this happens 100% of the time. This will prevent and avoid similar mishaps; regardless of time constraints or pressure to accomplish a task in a timely manner. A safety pause is necessary.