Electronic-bridge excitation of the 76 eV nuclear isomeric state in ^{235}U is shown to be strongly enhanced in the U^{7+} ion, potentially enabling laser excitation of this nucleus. This is because the electronic spectrum has a very high level density near the nuclear transition energy that ensures the resonance condition is fulfilled. We present a quantum statistical theory based on many-body quantum chaos to demonstrate that typical values for the electronic factor increase the probability of electronic bridge in ^{235}U^{7+} by many orders of magnitude. We also extract the nuclear matrix element by considering internal conversion from neutral uranium. The final electronic-bridge rate is comparable to the rate of the Yb^{+} octupole transition currently used in precision spectroscopy.