  In this work we construct a low-order nonconforming approximation method for
linear elasticity problems supporting general meshes and valid in two and three
space dimensions. The method is obtained by hacking the Hybrid High-Order
method, that requires the use of polynomials of degree $k\ge1$ for stability.
Specifically, we show that coercivity can be recovered for $k=0$ by introducing
a novel term that penalises the jumps of the displacement reconstruction across
mesh faces. This term plays a key role in the fulfillment of a discrete Korn
inequality on broken polynomial spaces, for which a novel proof valid for
general polyhedral meshes is provided. Locking-free error estimates are derived
for both the energy- and the $L^2$-norms of the error, that are shown to
convergence, for smooth solutions, as $h$ and $h^2$, respectively (here, $h$
denotes the meshsize). A thorough numerical validation on a complete panel of
two- and three-dimensional test cases is provided.
