  We apply Garnier's method to solve the Plateau problem for maximal surfaces
in Minkowski 3-space. Our study relies on the improved version we gave of R.
Garnier's resolution of the Plateau problem for polygonal boundary curves in
Euclidean 3-space. Since in Minkowski space the method does not allow us to
avoid the existence of singularities, the appropriate framework is to consider
maxfaces -- generalized maximal surfaces without branch points, introduced by
M. Umehara and K. Yamada. We prove that any given spacelike polygonal curve in
generic position in Minkowski 3-space bounds at least one maxface of disk-type.
This is a new result, since the only known result for the Plateau problem in
Minkowski space (due to N. Quien) deals with boundary curves of regularity
$C^{3,\alpha}$.
