A single primary-beam area centered on alpha=08h52m16s, Delta=+17d16' (1950.0) was surveyed with the Very Large Array at 1.452 GHz. The rms map noise is 0.030 + 0.001 mJy, and the resulting source list is complete to a map peak flux density S_p = 0.2 mJy within 25 arcmin of the field center. Source counts between 0.2 and 5 mJy were determined. Our best-fit model for the counts suggests that the faintest sources have absolute radio luminosities L < 10^24 W/Hz and do not evolve significantly. Sources stronger than 0.2 mJy appear to account for most of the radio-source background. The rms sky-temperature fluctuation in the central 10'x10' of the map is less than 0.029 K (>99% confidence) on an angular scale ~19 arcsec. This limit constrains theories which attribute the cosmic microwave background to thermalized radiation from massive pregalactic stars or bursts of star formation in young galaxies.