We have discovered an optically thick, edge-on circumstellar disk around a Herbig Ae star in the binary system PDS 144, providing the first intermediate-mass analog of HK Tau and similar T Tauri stars. This system consists of a V similar to 13 mag primary and a fainter companion, with the spectra of both stars showing evidence for circumstellar disks and accretion; both stars were classified as Herbig Ae by the Pico dos Dias Survey. In Lick adaptive optics polarimetry, we resolved extended polarized light scattered from dust around the northern star. Follow-up Keck adaptive optics and mid-infrared observations show that this star is entirely hidden by an optically thick disk at all wavelengths from 1.2 to 11.7 mu m. The disk major axis subtends similar to 0."8 on the sky, corresponding to similar to 800 AU at a distance of 1000 pc. Bright "wings'' extend 0."3 above and below the disk ansae, due most likely to scattering from the edges of an outflow cavity in a circumstellar envelope. We discuss the morphology of the disk and the spectral energy distributions of the two PDS 144 stars, present preliminary disk models, and identify a number of open questions regarding this fascinating system.