How sensitive is a neutrino factory to the angle θ₁₃?

We consider the impact of non-standard interactions of neutrinos (NSI) on the determination of neutrino mixing parameters at a neutrino factory using $\pnu{e}\to\pnu{\mu}$ ``golden channels'' for the measurement of $\theta_{13}$. We show how a small residual NSI leads to a drastic loss in sensitivity in $\theta_{13}$, of up to two orders of magnitude. This can be somewhat overcome if two baselines are combined.