Air carrier Captain reported a near ground collision with aircraft taxiing. Flight crew reported incident to ATC then proceeded with taxi clearance.

Narrative

Subject: Near collisionlocation: ORD Taxiway A14Date: Day 0Time: XA:42Incident description: near miss collision with Aircraft Y.(Ground 126.9) Taxi clearance was: 'Aircraft X A14; A; TT; HLD SHRT G.'Clearance was acknowledged and we proceeded at near Idle thrust to turn left into A14.Then revised taxi instructions: 'Give way to Aircraft Z on A' which was Aircraft Z coming from our left. Bringing the aircraft to a stop to give way. Well short of Taxiway A.For unknown reasons Aircraft Z remained stationary holding short of A14.At this time we were still holding short of A but not of B as our clearance was to give way to traffic on A.Then to our surprise Aircraft Y came from our right side southbound on Taxiway B; at which time I commented to the Ground Controller that this aircraft was approaching our position at considerable speed. At this time it was not sure he would clear our position without a collision; he cleared our radome by approximately 1.0 meter or 3 feet.The controller commented on Aircraft Y's action: 'he was not supposed to be doing that'We were stationary during this whole time.Aircraft A was following the first; which I communicated to the Ground Controller. Ground Controlmade him stop; and communicated to us that he was now holding short and clear of our position.We were then cleared to proceed on our taxi clearance with the mentioning that all tra'c was now giving way to us.We continued our taxi without further incidents.