Repeated imaging observations have been made of NGC 4527 with the Hubble Space Telescope between 1999 April and June, over an interval of 69 days. Images were obtained on 12 epochs in the F555W band and on five epochs in the F814W band. The galaxy hosted the Type Ia supernova SN 1991T, which showed relatively unusual behavior by having both an abnormal spectrum near light maximum, and a slower declining light curve than the prototypical Branch-normal SNe Ia. A total of 86 variables that are putative Cepheids have been found, with periods ranging from 7.4 days to over 70 days. From photometry with the DoPHOT program, the dereddened distance modulus is determined to be (m - M)0 = 30.67 ± 0.12 (internal uncertainty) using a subset of the Cepheid data whose reddening and error parameters are secure. A parallel analysis of the Cepheids using photometry with ROMAFOT yields (m - M)0 = 30.82 ± 0.11. The final adopted modulus is (m - M)0 = 30.74 ± 0.12 ± 0.12 (d = 14.1 ± 0.8 ± 0.8 Mpc). The photometric data for SN 1991T are used in combination with the Cepheid distance to NGC 4527 to obtain the absolute magnitude for this supernova of M(max) = -19.85 ± 0.29. The relatively large uncertainty is a result of the range in estimates of the reddening to the supernova. Thus, SN 1991T is seen to be only moderately brighter (by ~0.3 mag) than the mean for spectroscopically normal supernovae, although magnitude differences of up to 0.6 mag cannot be ruled out.