  We introduce and solve the one-dimensional quantum non-linear Schrodinger
(NLS) equation for an N-component field defined on the real line with a defect
sitting at the origin. The quantum solution is constructed using the quantum
inverse scattering method based on the concept of Reflection-Transmission (RT)
algebras recently introduced. The symmetry of the model is generated by the
reflection and transmission defect generators defining a defect subalgebra. We
classify all the corresponding reflection and transmission matrices. This
provides the possible boundary conditions obeyed by the canonical field and we
compute these boundary conditions explicitly. Finally, we exhibit a phenomenon
of spontaneous symmetry breaking induced by the defect and identify the
unbroken generators as well as the exact remaining symmetry.
