We report evidence for a recent burst of star formation located within 9 pc of the active nucleus of NGC 1097. The observational signatures of the starburst include UV absorption lines and continuum emission from young stars observed in a small-aperture HST spectrum. The burst is a few times 10^6 yr old, has a mass of approximately 10^6 solar masses, an observed luminosity of 1.5 x 10^7 solar luminosities and is obscured by approximately 3 visual magnitudes. The importance of this finding is two-fold: (1) the proximity of the starburst to the active nucleus and thus possible association with it; (2) its obscuration by and apparent association with a dusty absorbing medium, while the broad emission lines appear unobscured, suggesting that the starburst could be embedded in a circumnuclear torus as predicted in the Unified Model of active galactic nuclei.