Deep Swift UV/Optical Telescope (UVOT) imaging of the Chandra Deep Field South is used to measure galaxy number counts in three near ultraviolet (NUV) filters (uvw2: 1928 A, uvm2: 2246 A, uvw1: 2600 A) and the u band (3645 A). UVOT observations cover the break in the slope of the NUV number counts with greater precision than the number counts by the Hubble Space Telescope (HST) Space Telescope Imaging Spectrograph (STIS) and the Galaxy Evolution Explorer (GALEX), spanning a range from 21 < m_AB < 25. Number counts models confirm earlier investigations in favoring models with an evolving galaxy luminosity function.