We present rotation periods for 71 single dwarf members of the open cluster NGC 6811 determined using photometry from NASA's Kepler mission. The results are the first from The Kepler Cluster Study, which combines Kepler's photometry with ground-based spectroscopy for cluster membership and binarity. The rotation periods delineate a tight sequence in the NGC 6811 color-period diagram from ~1 day at mid-F to ~11 days at early-K spectral type. This result extends to 1Gyr similar prior results in the ~600Myr Hyades and Praesepe clusters, suggesting that rotation periods for cool dwarf stars delineate a well-defined surface in the three-dimensional space of color (mass), rotation, and age. It implies that reliable ages can be derived for field dwarf stars with measured colors and rotation periods, and it promises to enable further understanding of various aspects of stellar rotation and activity for cool stars.