We study the deformation theory of nearly G2 manifolds. These are seven dimensional manifolds admitting real Killing spinors. We show that the infinitesimal deformations of nearly G2 structures are obstructed in general. Explicitly, we prove that the infinitesimal deformations of the homogeneous nearly G2 structure on the Aloff--Wallach space are all obstructed to second order. We also completely describe the cohomology of nearly G2 manifolds.
