A320 pilot reported uncommanded pull to the left during the takeoff roll. Flight crew rejected the takeoff.

Narrative

After normal pushback and taxi; we observed no abnormalities prior to take-off. We accomplished all checklists and we taxied into position for take-off from Runway XX at ZZZ. Weather conditions at the time were winds 120/19 and VMC. I transferred the controls to the First Officer; and after given clearance to take-off; the First Officer advanced thrust. I observed normal engine and airspeed indications throughout the take-off roll. Passing 80 kts. all indications continued normal and the First Officer maintained directional control.Take-off data calculated V1 at 135 kts. Somewhere between 95-115 kts.; the aircraft pulled uncommanded to the left. The aircraft quickly departed the centerline of the runway at a rate that made the takeoff unsafe to continue. Deviation from centerline was approximately 20 feet left. There were no abnormal engine indications or ECAMs. I (Captain) called 'Reject' and took control of aircraft. I executed Rejected Take-off procedures; brought the aircraft to a safe stop; and advised the cabin to 'Remain Seated; Remain Seated'. After taxiing off the runway and setting the Parking Brake; I made appropriate calls to the cabin crew; a PA to the customers advising of our situation; and debriefed with the First Officer quickly on what happened and what he experienced from his perspective as Pilot-Flying at the time of the event. During this time we observed brake temperatures between 350-500 deg and Brake Fan was turned on. We then coordinated with ZZZ Operations to facilitate a gate return and to have Maintenance Control meet us. I documented the uncommanded left pulling and pertinent information into the Maintenance Logbook. I made an additional PA to the customers explaining of the abnormal experience and that Company was working on getting a new aircraft to continue our flight to ZZZ1.