Using the high-precision photometry from the Kepler space telescope, thousands of stars with stellar and planetary companions have been observed. The characterization of stars with companions is not always straightforward and can be contaminated by systematic and stellar influences on the light curves. Here, through a detailed analysis of starspots and eclipses, we identify KOI-1003 as a new, active RS CVn star---the first identified with data from Kepler. The Kepler light curve of this close binary system exhibits the systems primary transit, secondary eclipse, and starspot evolution of two persistent active longitudes. The near equality of the systems orbital and rotation periods indicates the orbit and primary stars rotation are nearly synchronized ($P_mathrm{orb} = 8.360613pm0.000003$ days; $P_mathrm{rot} sim 8.23$ days). By assuming the secondary star is on the main sequence, we suggest the system consists of a $1.45^{+0.11}_{-0.19} M_odot$ subgiant primary and a $0.59^{+0.03}_{-0.04} M_odot$ main-sequence companion. Our work gives a distance of $4400 pm 600$ pc and an age of $t = 3.0^{-0.5}_{+2.0}$ Gyr, parameters which are discrepant with previous studies that included the star as a member of the open cluster NGC 6791.
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