Stars in the core of 47 Tuc have been intensively surveyed for variability, using differential time series photometry, with the Planetary Camera of the Hubble Space Telescope. Some 20,000 stars were surveyed in the U band (F336W) in a 66 '' x 66 '' held centered on the core of 47 Tuc, with almost continuous observing over 38.5 hr, and using 1000 s exposure times. Using aperture photometry, PSF fitting, and power spectrum techniques, two W UMa systems were discovered, as well as six semidetached or detached binaries with periods between 0.41 and 1.5 days. The two faintest variables found are within the error circles of two highly variable X-ray sources and are good candidates for neutron star binaries or magnetic cataclysic variables. Two other certain variables were found, one of which is a possible cataclysmic variable. The radial distribution of the binaries is significantly more centrally concentrated than the average star, but it is consistent with the radial distribution of the blue stragglers found in the core. We show that the contact binary frequency and the period distribution of the binaries imply that few, if any, of the binaries are primordial.