The Hamburg/ESO quasar HE 1113-0641 is found to be a quadruple gravitational lens, based on observations with the twin 6.5m Magellan telescopes at the Las Campanas Observatory, and subsequently with the Hubble Space Telescope. The z_S=1.235 quasar appears in a cross configuration, with i band magnitudes ranging from 18.0 to 18.8. With a maximum image separation of 0.67, this is the smallest-separation quadruple ever identified using a ground-based optical telescope. PSF subtraction reveals a faint lensing galaxy. A simple lens model succeeds in predicting the observed positions of the components, but fails to match their observed flux ratios by up to a magnitude. We estimate the redshift of the lensing galaxy to be z_L~0.7. Time delay estimates are on the order of a day, suggesting that the flux ratio anomalies are not due to variability of the quasar, but may result from substructure or microlensing in the lens galaxy.