We present the first observation of subpicosecond electron bunches from an ultracold electron source. This source is based on near-threshold, two-step, femtosecond photoionization of laser-cooled rubidium gas in a grating magneto-optical trap. Bunch lengths as short as 735±7 fs (rms) have been measured in the self-compression point of the source by means of ponderomotive scattering of the electrons by a 25 fs, 800 nm laser pulse. The observed temporal structure of the electron bunch depends on the central wavelength of the ionization laser pulse, in agreement with detailed simulations of the atomic photoionization process. This shows that the bunch length limit imposed by the atomic photoionization process has been reached.</p