THE gas clouds of the interstellar medium have a fractal structure, the origin of which has generally been thought to lie in turbulence(1,2). The energy of turbulence could come from galactic rotation at large scale, then cascade down to be dissipated on small scales by viscosity(5,14); it has been suggested that such turbulence helps to prevent massive molecular clouds from collapsing in response to their own gravity(15,16). Here we show that, on the contrary, self-gravity itself may be the dominant factor in making clouds fractal. We develop a field-theory approach to the structure of clouds, assuming them to be isothermal, and with only gravitational interactions; we find that the observed fractal dimension of the clouds arises naturally from this approach. Although this result does not imply that turbulence is not important, it does demonstrate that the fractal structure can be understood without it.