Four fields in the young cluster NGC 2264 were monitored in Cousins I with a CCD on the 0.6 m telescope at Van Vleck Observatory during the 1995/96 observing season. A total of 209 stars were followed, reaching a limiting magnitude of about 16. Nine periodic variables were found and they are interpreted as spotted, pre-main-sequence stars with rotation periods ranging from 1.2 to 9.7 days. Three additional possible spotted variables, one with a period of only 0.71 days, and one possible eclipsing binary were also found. Comparing with the Orion Nebula Cluster (ONC), we find that there is a higher proportion of rapid rotators in NGC 2263 among stars with detected periods. Since the ONC sample is probably younger, this may be evidence for spin-up of most pre-main-sequence stars as they contract towards the main sequence. If this interpretation is correct, it suggests that disk braking may not be important for most stars beyond an age of similar to 1 million years. (C) 1997 American Astronomical Society.