Narrative:

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.

Google
 

Original NASA ASRS Text

Title: 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.

Narrative: 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.

Data retrieved from NASA's ASRS site as of July 2013 and automatically converted to unabbreviated mixed upper/lowercase text. This report is for informational purposes with no guarantee of accuracy. See NASA's ASRS site for official report.