A two-dimensional (2D) optical coherent spectroscopy that correlates the double excited electronic states to constituent single excited states is described. The technique, termed two-dimensional double-quantum coherence spectroscopy (2D-DQCS), makes use of multiple, time-ordered ultrashort coherent optical pulses to create double and single quantum coherences over the time intervals between the pulses. The resulting 2D electronic spectra map out the energy correlation between the first excited state and two-photon-allowed double-quantum states. Measurements of organic dye molecules show that the near-resonant energy offset for adding a second electronic excitation to the system relative to the first excitation is oil the order of tens of millielectronvolts. Simulations of DQC spectra show that vibronic transitions add rich features to the 2D spectra. The results of quantum chemical calculations on model systems provide insight into the many-body origin of the energy shift measured in the experiment. These results demonstrate the potential of 2D-DQCS for elucidating quantitative information about electron-electron interactions, many-electron wave functions, and electron correlation in electronic excited states and excitons.