Spiral galaxies must acquire gas to maintain their observed level of star formation beyond the next few billion years(1). A source of this material may be the gas that resides between galaxies, but our understanding of the state and distribution of this gas is incomplete(2). Radio observations(3) of the Local Group of galaxies have revealed hydrogen gas extending from the disk of the galaxy M31 at least halfway to M33. This feature has been interpreted to be the neutral component of a condensing intergalactic filament(4), which would be able to fuel star formation in M31 and M33, but simulations suggest that such a feature could also result from an interaction between both galaxies within the past few billion years (ref. 5). Here we report radio observations showing that about 50 per cent of this gas is composed of clouds, with the rest distributed in an extended, diffuse component. The clouds have velocities comparable to those of M31 and M33, and have properties suggesting that they are unrelated to other Local Group objects. We conclude that the clouds are likely to be transient condensations of gas embedded in an intergalactic filament and are therefore a potential source of fuel for future star formation in M31 and M33.