  We present a reduced basis (RB) method for parametrized linear elliptic
partial differential equations (PDEs) in a least-squares finite element
framework. A rigorous and reliable error estimate is developed, and is shown to
bound the error with respect to the exact solution of the PDE, in contrast to
estimates that measure error with respect to a finite-dimensional
(high-fidelity) approximation. It is shown that the first-order formulation of
the least-squares finite element is a key ingredient. The method is
demonstrated using numerical examples.
