In recent years, millimeter wavelength observations of protoplanetary disks around young stars have revealed substructures. These structures include asymmetries, gaps, and rings that could be indicative of phenomena creating gas pressure maxima which trap large dust grains, aiding their growth and promoting planet formation. The congregation and growth of large dust grains is thought to be a critical step in the grain growth that allows planets to form in the relatively short time frame before the circumstellar disk dissipates. We present new, high-resolution Sub-Millimeter Array observations (at a wavelength of 1.3 mm) of the HD 34700 system. The multiple Herbig Ae system HD 34700 is comprised of a close central binary and a distant companion, and has a bright disk around its central binary inferred through its strong infrared and millimeter excess. Recent scattered light observations showed that the smaller dust grains form a spiral arm structure with a large central cavity and an azimuthal discontinuity. Our SMA observations show an azimuthal asymmetry in the dust continuum which is indicative of a dust trap: a strong concentration of larger dust grains toward a likely pressure maximum in the gas. The trap is located at approximately 167 au from the central binary and with an azimuthal extent of 24 degrees. This is confirmed by our detection of CO gas centered on the binary location and consistent with a standard Keplerian disk. The large dust asymmetry could be produced by a planet producing a vortex at the cavity’s edge, or by the dynamical interactions of the central binary. Finally, we also detect a previously-unknown small dust disk around the distant companion HD 34700B, with a radius of approximately 43 au.