We have conducted a deep, complete HI survey, using Arecibo/ALFA, of a field centered on the nearby, isolated galaxy, NGC 2903, which is similar to the Milky Way in its properties. The field size was 150 kpc x 260 kpc and the final velocity range spanned from 100 to 1133 km/s. The ALFA beams have been mapped as a function of azimuth and cleaned from each azimuth-specific cube prior to forming final cubes. The final HI data are sensitive down to an HI mass of 2 x 10^5 Mo and column density of 2 x 10^{17} cm^{-2} at the 3sigma x 2deltaV level, where sigma is the rms noise level and deltaV is the velocity resolution. NGC 2903 is found to have an HI envelope that is larger than previously known, extending to at least 3 times the optical diameter of the galaxy. Our search for companions yields one new discovery with an HI mass of 2.6 x 10^6 Mo. The companion is 64 kpc from NGC 2903 in projection, is likely associated with a small optical galaxy of similar total stellar mass, and is dark matter dominated, with a total mass >10^8 Mo. In the region surveyed, there are now two known companions: our new discovery and a previously known system that is likely a dwarf spheroidal, lacking HI content. If HI constitutes 1% of the total mass in all possible companions, then we should have detected 230 companions, according to LCDM predictions. Consequently, if this number of dark matter clumps are indeed present, then they contain less than 1% HI content, possibly existing as very faint dwarf spheroidals or as starless, gasless dark matter clumps.
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