Colloidal gelation has been extensively studied for the case of purely attractive systems, but little is understood about how colloidal gelation is affected by the presence of repulsive interactions. Here we demonstrate the gelation of a binary system of oppositely charged colloids, in which repulsive interactions compete with attractive interactions. We observe that gelation is controlled by varying the total volume fraction, the interaction strength, and the new tuning parameter of the mixing ratio of the two particle types, and present a state diagram of gelation along all these phase-space coordinates. Contrary to commonly studied purely attractive gels, in which weakly quenched gels are more compact and less tenuous, we find that particles in these binary gels form fewer contacts and the gels become more tenuous as we approach the gel point. This suggests that a different mechanism governs gel formation and ultimate structure in binary gelation: particles are unable to form additional favorable contacts through rearrangements, due to the competition of repulsive interactions between similarly charged colloids and attractive interactions between oppositely charged colloids.