  We establish a general normal subgroup theorem for commensurators of lattices
in locally compact groups. While the statement is completely elementary, its
proof, which rests on the original strategy of Margulis in the case of higher
rank lattices, relies heavily on analytic tools pertaining to amenability and
Kazhdan's property (T). It is a counterpart to the normal subgroup theorem for
irreducible lattices of Bader and the second named author, and may also be used
to sharpen that result when one of the ambient factors is totally disconnected.
