We present a 93 \arcmin~ { } \times~ { } 93 \arcmin map of the area near the Local Group dwarf galaxy LGS 3 , centered on an H I cloud 30′ away from the galaxy . Previous authors associated this cloud with LGS 3 but relied on observations made with a 36′ beam . Our high-resolution ( 3 \farcm 4 ) , wide-field Arecibo observations of the region reveal that the H I cloud is distinct from the galaxy and suggest an interaction between the two . We point out faint emission features in the map that may be gas that has been tidally removed from the H I cloud by LGS 3 . We also derive the rotation curve of the cloud and find that it is in solid-body rotation out to a radius of 10′ , beyond which the rotation velocity begins to decline . Assuming a spherical geometry for the cloud , the implied mass is 2.8 \times 10 ^ { 7 } ( d / \mbox { Mpc } ) M _ { \odot } , where d is the distance in Mpc . The observed H I mass is 5.5 \times 10 ^ { 6 } ( d / \mbox { Mpc } ) ^ { 2 } M _ { \odot } , implying that the cloud is dark-matter dominated unless its distance is at least 1.9 Mpc . We propose that the cloud is a high-velocity cloud that is undergoing a tidal interaction with LGS 3 and therefore is located roughly 700 kpc away from the Milky Way . The cloud then contains a total mass of \sim 2.0 \times 10 ^ { 7 } M _ { \odot } , 82 % of which consists of dark matter .