B737 First Officer reported a fuel imbalance during climbout. Crew ran fuel leak checklist and returned to the departure airport after shutting done an engine.

Narrative

When we started in ZZZ our fuel was 19;000lbs with 2;000 lbs in the center tank. We took off from Runway XXL on the ZZZZZ departure; ZZZZZ1 transition. After receiving vectors initially we were given direct ZZZZZ2. climbing through FL180 Captain A alerted me to a fuel imbalance notification under the left fuel indicator. We both witnessed the fuel dropping at a rate of 100lbs every 15-20 seconds. At this point we asked ZZZ for a level off at FL200 while we ran the appropriate checklist. At this point the imbalance was about 1;100lbs. The Captain asked the flight attendants to look out the left side of the aircraft for any indications of a fuel leak; and they reported back not seeing anything. We ran the NG Fuel Leak Checklist. At step X we started a timer and noted the current fuel in the left tank. Within 1.5-2 minutes we had lost more than the 500lbs the checklist calls for. At this point we [requested priority handling]; shut down the left engine (per the checklist); and completed the checklist. We returned to ZZZ and performed the ILS XYR approach. We taxied to Gate XX after an uneventful landing.