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We present the results of a survey for Cepheid variables in the Virgo Cluster spiral NGC 4571 using the High-Resolution Camera (HRCam) on the Canada-France-Hawaii Telescope. Our 13 epochs, taken over a span of $\sim$ 800 days, have typical FWHM of 0.50 arcsec enabling 10\% photometry to R $\sim$ 24.5 mag. The application of point-spread-function fitting photometry and both an automated and visual search for variability has resulted in the identification of several variables. Three of the most isolated have periods and colors indicative of Cepheids. These variables have periods in the range of 50 to 90 days and mean R magnitudes of 24.3 to 23.5 mag.
Adopting an absolute calibration based upon Cepheids in the LMC (m--M = 18.5 $\pm$ 0.08 mag) yields a mean apparent R-band distance modulus of (m--M)$_A = 30.91 \pm 0.15$ mag, with the uncertainty resulting from both the finite width of the instability strip and that in the absolute distance of the LMC. With the assumption that the Cepheids in NGC 4571 suffer only from Galactic extinction (A$_R$ = 0.04 mag) we conclude that the true distance is 14.9 $\pm$ 1.2 Mpc. Given that NGC 4571 is within 2.$^\circ$5 of M 87, is severely stripped of H I, and has a radial velocity of only 342 km s$^{-1}$ (implying that it is moving through the cluster core along the line-of-sight), we argue that this distance is also representative of the Virgo Cluster ``core''
The derived distance is in good agreement with the majority of modern methods of estimating extragalactic distances and suggests that the extragalactic distance scale is now established. Adopting a Coma to Virgo distance ratio of 5.5, from a variety of methods, we find H$_\circ = 87 \pm 7$ km s$^{-1}$ Mpc$^{-1}$. The cosmological implications of this result are briefly discussed.
