  We consider 3d N>= 2 superconformal field theories on a branched covering of
a three-sphere. The Renyi entropy of a CFT is given by the partition function
on this space, but conical singularities break the supersymmetry preserved in
the bulk. We turn on a compensating R-symmetry gauge field and compute the
partition function using localization. We define a supersymmetric observable,
called the super Renyi entropy, parametrized by a real number q. We show that
the super Renyi entropy is duality invariant and reduces to entanglement
entropy in the q -> 1 limit. We provide some examples.
