We use three different statistical models describing the frequency of meteoroid impacts on Earth to estimate the seismic background noise due to impacts on the lunar surface. Because of diffraction, seismic events on the Moon are typically characterized by long codas, lasting 1 h or more. We find that the small but frequent impacts generate seismic signals whose codas overlap in time, resulting in a permanent seismic noise that we term the "lunar hum'' by analogy with the Earth's continuous seismic background seismic hum. We find that the Apollo era impact detection rates and amplitudes are well explained by a model that parameterizes (1) the net seismic impulse due to the impactor and resulting ejecta and (2) the effects of diffraction and attenuation. The formulation permits the calculation of a composite waveform at any point on the Moon due to simulated impacts at any epicentral distance. The root-mean-square amplitude of this waveform yields a background noise level that is about 100 times lower than the resolution of the Apollo long-period seismometers. At 2 s periods, this noise level is more than 1000 times lower than the low noise model prediction for Earth's microseismic noise. Sufficiently sensitive seismometers will allow the future detection of several impacts per day at body wave frequencies.