With the Deep Underground Neutrino Experiment (DUNE) as an example, we show that the presence of even one sterile neutrino of mass $sim$1 eV can significantly impact the measurements of CP violation in long baseline experiments. Using a probability level analysis and neutrino-antineutrino asymmetry calculations, we discuss the large magnitude of these effects, and show how they translate into significant event rate deviations at DUNE. Our results demonstrate that measurements which, when interpreted in the context of the standard three family paradigm, indicate CP conservation at long baselines, may, in fact hide large CP violation if there is a sterile state. Similarly, any data indicating the violation of CP cannot be properly interpreted within the standard paradigm unless the presence of sterile states of mass O(1 eV) can be conclusively ruled out. Our work underscores the need for a parallel and linked short baseline oscillation program and a highly capable near detector for DUNE, in order that its highly anticipated results on CP violation in the lepton sector may be correctly interpreted.
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