Repeated imaging observations have been made of NGC 3627 with the Hubble Space Telescope in 1997 - 1998 over an interval of 58 days. Images were obtained on 12 epochs in the F555W band and on five epochs in the F814W band. The galaxy hosted the prototypical, "Branch normal," type Ia supernova SN 1989B. A total of 83 variables have been found, of which 68 are definite Cepheid variables with periods ranging from 75 to 3.85 days. The dereddened distance modulus is determined to be (m-M)o=30.22{+/-}0.12 (internal uncertainty) using a subset of the Cepheid data whose reddening and error parameters are secure.