  We define and analyse a least-squares finite element method for a first-order
reformulation of the obstacle problem. Moreover, we derive variational
inequalities that are based on similar but non-symmetric bilinear forms. A
priori error estimates including the case of non-conforming convex sets are
given and optimal convergence rates are shown for the lowest-order case. We
provide also a posteriori bounds that can be be used as error indicators in an
adaptive algorithm. Numerical studies are presented.
