B737-700
Flight Crew Instrument; Flight Crew Multiengine; Flight Crew Air Transport Pilot (ATP)
Situational Awareness; Distraction
Conflict Ground Conflict; Critical; Deviation / Discrepancy - Procedural Published Material / Policy
Air Traffic Control Issued Advisory / Alert; Flight Crew Took Evasive Action
Human Factors
Under positive control of Ground Control; we were cleared to push from [the] Gate onto Taxiway A. We subsequently were cleared to taxi northeast bound on A; and my First Officer (FO) physically looked right; and stated 'Clear right.' We were approaching the taxi line at about a thirty degree angle when I heard Ground Control broadcast to a light aircraft; 'I told you to give way to Company.' I looked to our right; and saw a small aircraft; veering away from us; and passing on our right; maybe forty feet away. I was startled by the unexpected appearance of an aircraft passing us; and thankfully was only moving at perhaps less than eight knots ground speed; on a single engine taxi with minimal 32% thrust; when I saw the aircraft; so I only had to decelerate slightly to allow the aircraft safely pass. Ground Control gave the other aircraft a slight verbal admonishment; and we continued our taxi as instructed.
Boeing 737 Captain reported a ground conflict with an aircraft that had not followed ATC instruction.