Can nonstandard interactions jeopardize the hierarchy sensitivity of DUNE?

We study the effect of nonstandard interactions (NSIs) on the propagation of neutrinos through the Earth's matter and how it affects the hierarchy sensitivity of the DUNE experiment. We emphasize the special case when the diagonal NSI parameter ϵee=-1, nullifying the standard matter effect. We show that if, in addition, CP violation is maximal then this gives rise to an exact intrinsic hierarchy degeneracy in the appearance channel, irrespective of the baseline and energy. Introduction of the off diagonal NSI parameter, ϵeτ, shifts the position of this degeneracy to a different ϵee. Moreover the unknown magnitude and phases of the off diagonal NSI parameters can give rise to additional degeneracies. Overall, given the current model independent limits on NSI parameters, the hierarchy sensitivity of DUNE can get seriously impacted. However, a more precise knowledge of the NSI parameters, especially ϵee, can give rise to an improved sensitivity. Alternatively, if a NSI exists in nature, and still DUNE shows hierarchy sensitivity, certain ranges of the NSI parameters can be excluded. Additionally, we briefly discuss the implications of ϵee=-1 (in the Earth) on the Mikheyev-Smirnov-Wolfenstein effect in the Sun.