The low-lying energy levels of proton-rich ^ { 56 } Cu have been extracted using in-beam \gamma -ray spectroscopy with the state-of-the-art \gamma -ray tracking array GRETINA in conjunction with the S800 spectrograph at the National Superconducting Cyclotron Laboratory at Michigan State University . Excited states in ^ { 56 } Cu serve as resonances in the ^ { 55 } Ni ( p , \gamma ) ^ { 56 } Cu reaction , which is a part of the rp-process in type I x-ray bursts . To resolve existing ambiguities in the reaction Q-value , a more localized IMME mass fit is used resulting in Q = 639 \pm 82 keV . We derive the first experimentally-constrained thermonuclear reaction rate for ^ { 55 } Ni ( p , \gamma ) ^ { 56 } Cu . We find that , with this new rate , the rp-process may bypass the ^ { 56 } Ni waiting point via the ^ { 55 } Ni ( p , \gamma ) reaction for typical x-ray burst conditions with a branching of up to \sim 40 \% . We also identify additional nuclear physics uncertainties that need to be addressed before drawing final conclusions about the rp-process reaction flow in the ^ { 56 } Ni region .