Compared to their centimeter-wavelength counterparts, millimeter recombination lines (RLs) are intrinsically brighter and are free of pressure broadening. We report observations of RLs (H30alpha at 231.9 GHz, H53alpha at 42.9 GHz) and the millimeter and centimeter continuum toward the Becklin-Neugebauer (BN) object in Orion, obtained from the Atacama Large Millimeter/submillimeter Array (ALMA) Science Verification archive and the Very Large Array (VLA). The RL emission appears to be arising from the slowly-moving, dense (Ne=8.4x10^6 cm^-3) base of the ionized envelope around BN. This ionized gas has a relatively low electron temperature (Te<4900 K) and small (<<10 km s^-1) bulk motions. Comparing our continuum measurements with previous (non)detections, it is possible that BN has large flux variations in the millimeter. However, dedicated observations with a uniform setup are needed to confirm this. From the H30alpha line, the central line-of-sight LSR velocity of BN is 26.3 km s^-1.