The Green Bank Telescope has been used to search for 21cm H I emission over a large area between the galaxies M31 and M33 in an attempt to confirm at 9 \farcm 1 angular resolution the detection by Braun & Thilker ( 4 ) of a very extensive neutral gas “ bridge ” between the two systems at the level N _ { HI } \approx 10 ^ { 17 } cm ^ { -2 } . We detect H I emission at several locations up to 120 kpc in projected distance from M31 , at least half the distance to M33 , with velocities similar to that of the galaxies , confirming the essence of the Braun & Thilker discovery . The H I does not appear to be associated with the extraplanar high-velocity clouds of either galaxy . In two places we measure N _ { HI } > 3 \times 10 ^ { 18 } cm ^ { -2 } , indicative of concentrations of H I with \sim 10 ^ { 5 } M _ { \odot } on scales \lesssim 2 kpc , but over most of the field we have only 5 \sigma upper limits of N _ { HI } \leq 1.4 \times 10 ^ { 18 } cm ^ { -2 } . In very deep measurements in two directions H I lines were detected at a few 10 ^ { 17 } cm ^ { -2 } . The absence of emission at another location to a 5 \sigma limit N _ { HI } \leq 1.5 \times 10 ^ { 17 } cm ^ { -2 } suggests that the H I bridge is either patchy or confined to within \sim 125 kpc of M31 . The measurements also cover two of M31 ’ s dwarf galaxies , And II and And XV , but in neither case is there evidence for associated H I at the 5 \sigma level of 1.4 \times 10 ^ { 4 } M _ { \odot } for And II , and 9.3 \times 10 ^ { 3 } M _ { \odot } for And XV .