  We study parameter degeneracies that can occur in long-baseline neutrino
appearance experiments due to nonstandard interactions (NSI) in neutrino
propagation. For a single off-diagonal NSI parameter, and neutrino and
antineutrino measurements at a single L/E, there exists a continuous four-fold
degeneracy (related to the mass hierarchy and $\theta_{23}$ octant) that
renders the mass hierarchy, octant, and CP phase unknowable. Even with a
combination of NO$\nu$A and T2K data, which in principle can resolve the
degeneracy, both NSI and the CP phase remain unconstrained because of
experimental uncertainties. A wide-band beam experiment like DUNE will resolve
this degeneracy if the nonzero off-diagonal NSI parameter is $\epsilon_{e\mu}$.
If $\epsilon_{e\tau}$ is nonzero, or the diagonal NSI parameter $\epsilon_{ee}$
is O(1), a wrong determination of the mass hierarchy and of CP violation can
occur at DUNE. The octant degeneracy can be further complicated by
$\epsilon_{e\tau}$, but is not affected by $\epsilon_{ee}$.
