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Very sensitive 21cm HI measurements have been made at several locationsaround the Local Group galaxy M31 using the Green Bank Telescope (GBT) at anangular resolution of 9.1', with a 5$\sigma$ detection level of $\rm{N_{HI} =3.9 \times 10^{17}~cm^{-2}}$ for a 30 $\rm{km~s^{-1}}$ line. Most of the HI ina 12 square degree area almost equidistant between M31 and M33 is contained innine discrete clouds that have a typical size of a few kpc and HI mass of$10^5$ M$_{\odot}$. Their velocities in the Local Group Standard of Rest liebetween -100 and +40 $\rm{km~s^{-1}}$, comparable to the systemic velocities ofM31 and M33. The clouds appear to be isolated kinematically and spatially fromeach other. The total HI mass of all nine clouds is $1.4 \times 10^6$M$_{\odot}$ for an adopted distance of 800 kpc with perhaps another $0.2 \times10^6$ M$_{\odot}$ in smaller clouds or more diffuse emission. The HI mass ofeach cloud is typically three orders of magnitude less than the dynamical(virial) mass needed to bind the cloud gravitationally. Although they have thesize and HI mass of dwarf galaxies, the clouds are unlikely to be part of thesatellite system of the Local Group as they lack stars. To the north of M31,sensitive HI measurements on a coarse grid find emission that may be associatedwith an extension of the M31 high-velocity cloud population to projecteddistances of $\sim 100$ kpc. An extension of the M31 high-velocity cloudpopulation at a similar distance to the south, toward M33, is not observed.

Sensitive 21cm Observations of Neutral Hydrogen in the Local Group near M31