  We give a formulation of linearized 11D supergravity in 4D, $N=1$ superspace
keeping all eleven bosonic coordinates. The fields are fluctuations around
$\mathbf M=\mathbf R^{4|4}\times Y$, where $Y$ is a background Riemannian
7-manifold admitting a $G_2$ structure. We embed the 11D fields into superfield
representations of the 4D, $N=1$ superconformal algebra. These consist of the
conformal graviton superfield, seven conformal gravitino superfields, a tensor
hierarchy of superfields describing the 11D 3-form, and a non-abelian
Kaluza-Klein vector multiplet gauging the tensor hierarchy by diffeomorphisms
on $Y$. The quadratic action consists of the linearization of a superspace
volume term and a Chern-Simons action for the gauged hierarchy coupled to the
supergravity and gravitino superfields, and the full structure is fixed by
superconformal and gauge invariance. When this action is projected to
components, we recover the full linearized action of 11D supergravity.
