We study the stability of the dislocation-free Bragg glass phase in a
layered geometry consisting of coupled parallel planes of d = 1 + 1 vo
rtex lines lying within each plane, in the presence of impurity disord
er. Using renormalization group, replica variational calculations and
physical arguments, we find that at temperatures T < T-G the 3D Bragg
glass phase is always stable for weak disorder. It undergoes a weakly
first-order transition into a decoupled 2D vortex glass upon increase
of disorder.