B737-700
Flight Crew Multiengine; Flight Crew Instrument; Flight Crew Commercial
Flight Crew Last 90 Days 477
Confusion; Communication Breakdown
Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance
Flight Crew Returned To Clearance
Human Factors; Chart Or Publication; Procedure
While in cruise flight on the SERFR 3 Arrival; Oakland Center cleared us direct to the NRRLI way point.  We mistakenly selected the NARWL way point and began navigating to that fix. After a minute; ATC queried our track and asked if we were going to NRRLI. Recognizing our error; we reprogrammed the FMC to change our course for NRRLI. ATC indicated that this was a common error and that they were in the process of making a change to the arrival.  In the future; I will be more aware of this deviation while on the SERFR Arrival and be careful before making any changes to fixes in the FMC.
B737 First Officer reported navigating to wrong; similar sounding; waypoint on STAR.