Absolute rate coefficients for dielectronic recombination (DR) of hydrogenlike U⁹¹⁺ have been measured at GSI's heavy-ion storage ring ESR in the center-of-mass energy range 63-90 keV. We find an excellent agreement between the measured DR rate coefficients and theoretical results from multi-configuration Dirac-Fock theory which includes the Breit interaction. The latter contributes nearly one half to the total resonance strengths of the KL_1/2L1/2 and KL_1/2M1/2 resonance groups.