Date: 202109
Local time of day: 1201-1800
Location: ZZZ.ARTCC, US
Aircraft: Commercial Fixed Wing
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Mission: Passenger
Flight phase: Climb; Initial Climb
Airspace: Class A ZZZ
ATC / advisory: Center ZZZ
Aircraft component: Fuel System
Component problem: Malfunctioning
Reporter organization: Air Carrier
Reporter function: Pilot Flying; First Officer
Reporter qualification: Flight Crew Instrument; Flight Crew Air Transport Pilot (ATP); Flight Crew Multiengine
Human factors: Troubleshooting; Time Pressure; Situational Awareness; Distraction; Confusion; Workload
Second reporter function: Captain; Pilot Flying
Anomaly: Aircraft Equipment Problem Critical; Inflight Event / Encounter Fuel Issue
Detector: Automation Aircraft Other Automation; Person Flight Crew
When detected: In-flight
Result: Flight Crew Requested ATC Assistance / Clarification; Flight Crew Landed in Emergency Condition; Flight Crew FLC complied w / Automation / Advisory; Flight Crew Returned To Departure Airport
Contributing factors: Aircraft
Primary problem: Aircraft

Narrative: On climbout of ZZZ Flight ABC we experienced a 1000 pound differential between main tanks on initial departure/climb-out.  The Captain pointed to the wing fuel quantity indicators and the left was amber indicating an imbalance between wing tanks.  We were on center tank feed so no fuel should be used in this condition.  I continued flying to a level off at FL260 and the CA ran the QRH for a fuel imbalance followed by the me backing him up by going through the QRH to confirm our situation. The CA plotted our fuel to the next waypoint which was ZZZZZ and were 1000 lbs below planned. Within a few minutes our fuel was 1500 lbs below planned fuel to the next waypoint ZZZZZ. The decision was made to request priority handling; shutdown engine #1 per the QRH; and return to ZZZ.   I ran the non normal checklists; cleanup items; and reviewed the evacuation checklist. The CA flew the approach and landing which were uneventful; stopped the aircraft on the runway; and had ARFF check for a visible leak. After confirmation that there were no fuel leaks we taxied the aircraft to parking and shutdown the aircraft normally.There are no causal factors by me that played a role in the event.I believe an aircraft history should be pulled to check for any history of fuel quantity malfunctions or any fuel system maintenance has been   completed for this this tail number.


Second narrative: Fuel imbalance developed during climb of 1000 lbs - left wing low within minutes of departure. Leaving 10;000 feet. Cabin crew was asked to perform a cabin walk through with attention paid to possible fuel emissions visible aft of wing from No.1 engine. No visible fuel leak was evident as communicated by cabin crew. We stopped climb at FL260. Position; time and fuel comparison with Flight Plan Review showed us 1000 lbs low at first fix after level off as we ran QRH IMBAL checklist. Subsequent FMC PROG fix (fix name: ZZZZZ) initially showed us estimating 1000 lbs low crossing the fix; then 1500 lbs low; then 1700 lbs low as we approached ZZZZZ. FMC PROG fuel estimate deterioration occurred rapidly over the course of just a few minutes. QRH IMBAL checklist led to Fuel Leak Engine Checklist - parameters indicated probable fuel leak No.1 engine - which led to Engine No. 1 shutdown. All checklists to include precautionary landing checklist were performed. ATC and Dispatch notified. Flight attendants and Passengers advised of return to ZZZ for a precautionary landing.  Single engine landing was performed - Captain flying. After landing we stopped on the runway; ARFF inspected aircraft; found no leaks or damage; and we taxied to the gate. The following AML entries were made: 1) possible fuel leak leading to engine No. 1 shutdown; 2) info to maintenance item: No 1 engine windmilling time 15 minutes; 3) info to maintenance item: landing was accomplished below maximum landing weight. Report made to Dispatch of engine failure and emergency declaration. FO did a great job - especially so given his approx 100 hours in seat and on type. Comment: cabin crew kept cool and were professional. Comment: I made every effort to be both clear and deliberate during each step of the event; to solicit FO's input; and - as we returned to ZZZ - I slowed the aircraft approximately 20 miles from the field and kept the cockpit CRM 'in the green' to the maximum extent possible.


Synopsis: B737-800 flight crew reported a fuel imbalance after departure. The crew ran the QRH checklist and determined there was a possible fuel leak. The crew made the decision to shutdown the suspect engine and return to their departure airport for maintenance.