  We solve the classical problem of Plateau in the setting of proper metric
spaces. Precisely, we prove that among all disc-type surfaces with prescribed
Jordan boundary in a proper metric space there exists an area minimizing disc
which moreover has a quasi-conformal parametrization. If the space supports a
local quadratic isoperimetric inequality for curves we prove that such a
solution is locally H\"older continuous in the interior and continuous up to
the boundary. Our results generalize corresponding results of Douglas and
Morrey from the setting of Euclidean space and Riemannian manifolds to that of
proper metric spaces.
