B737-700
Flight Crew Last 90 Days 212
Communication Breakdown
ATC Issue All Types; Conflict Airborne Conflict
Air Traffic Control Issued New Clearance; Flight Crew Took Evasive Action
Human Factors; Procedure
Flight requested climb from FL360 to FL380. Aircraft was on division line between [two ATC] Centers. Center advised a short delay. [Controller] subsequently cleared us to climb to FL380. Passing through FL365; flight crew detected Traffic Alert TA on map display and visually acquired traffic opposite direction at FL370 and at 10 o'clock position. Crew initiated right turn to increase separation and advised [Center] of conflict. [Center] advised both aircraft to turn 30 degrees right immediately. Suspect loss of separation at altitude.Crew suspects two possible causes of event. Most likely is a controller error by Center. [Center] may not have correctly accounted for inbound other carrier's aircraft arriving from [adjacent] airspace. Another possibility is that Crew took climb clearance from FL360 to FL380 that was intended for another aircraft and that the incorrect climb readback was not detected by Center. A Company Flight Number was also heard on Center once we were handed off to new Center.
The Controller concluded with; 'Thanks for your help.' We were neither told to call anyone nor told to call a controller by any ATC agency the entire flight about the event.
B737-700 flight crew reported airborne conflict and a TCAS TA in climb to FL380. Captain speculated either ATC error or readback/hearback contributed to the event.