We present a calculation of the leading SU(3)-breaking O(p(3)) corrections to the electromagnetic moments and charge radius of the lowest-lying decuplet resonances in covariant chiral perturbation theory. In particular, the magnetic dipole moment of the members of the decuplet is predicted fixing the only low-energy constant (LEC) present up to this order with the well-measured magnetic dipole moment of the Omega(-). We predict mu(++)(Delta) = 6.04(13) and mu(+)(Delta) = 2.84(2), which agree well with the current experimental information. For the electric quadrupole moment and the charge radius, we use state-of-the-art lattice QCD results to determine the corresponding LECs, whereas for the magnetic octupole moment there is no unknown LEC up to the order considered here, and we obtain a pure prediction. We compare our results with those reported in large N-c, lattice QCD, heavy-baryon chiral perturbation theory, and other models.