The Hubble Space Telescope Key Project on the Extragalactic Distance Scale.: XI.: The Cepheids in NGC 4414

We report the discovery of Cepheid variable stars in the galaxy NGC 4414, as part of the Hubble Space Telescope (HST) Key Project on the Extragalactic Distance Scale. Observations were obtained with the HST Wide-Field and Planetary Camera 2 (WFPC2) for 13 epochs at V (F555W) and 4 at I (F814W). Photometry was performed using two independent programs, DoPHOT and DAOPHOT/ALLFRAME. We find 11 Cepheids with high-quality light curves and well-determined periods of 19-70 days. Nine of these Cepheids are used in fitting the period-luminosity relation. Assuming an LMC distance modulus of 18.50 mag and E(B-V) = 0.10 mag, we derive a reddening-corrected distance modulus for NGC 4414 of 31.41 +/- 0.17 (random) +/- 0.16 (systematic) mag, corresponding to a distance of 19.1 +/- 1.5 (random) +/- 1.4 (systematic) Mpc. We derive a mean color excess for NGC 4414 of E(V-I) = 0.02 +/- 0.05 mag. NGC 4414 is a calibrator of the Tully-Fisher and Type Ia supernova secondary distance indicators, and we briefly discuss the implications of the new distance for these methods.