A supersymmetric Randall–Sundrum brane-world demands that not merely the graviton but the entire supergravity multiplet be trapped on the brane. To demonstrate this, we present a complete ansatz for the reduction of (D=5, N=4) gauged supergravity to (D=4, N=2) ungauged supergravity in the Randall–Sundrum geometry. We verify that it is consistent to lowest order in fermion terms. In particular, we show how the graviphotons avoid the ‘no photons on the brane’ result because they do not originate from Maxwell's equations in D=5 but rather from odd-dimensional self-duality equations. In the case of the fivebrane, the Randall–Sundrum mechanism also provides a new Kaluza–Klein way of obtaining chiral supergravity starting from non-chiral.