We present spectra and light curves of SNLS 06D4eu and SNLS 07D2bv, two hydrogen-free superluminous supernovae (SNe) discovered by the Supernova Legacy Survey. At z = 1.588, SNLS 06D4eu is the highest redshift superluminous SN with a spectrum, at MU = -22.7 it is one of the most luminous SNe ever observed, and it gives a rare glimpse into the rest-frame ultraviolet where these SNe put out their peak energy. SNLS 07D2bv does not have a host galaxy redshift, but on the basis of the SN spectrum, we estimate it to be at z ~ 1.5. Both SNe have similar observer-frame griz light curves, which map to rest-frame light curves in the U band and UV, rising in ~20 rest-frame days or longer and declining over a similar timescale. The light curves peak in the shortest wavelengths first, consistent with an expanding blackbody starting near 15,000 K and steadily declining in temperature. We compare the spectra with theoretical models, and we identify lines of C II, C III, Fe III, and Mg II in the spectra of SNLS 06D4eu and SCP 06F6 and find that they are consistent with an expanding explosion of only a few solar masses of carbon, oxygen, and other trace metals. Thus, the progenitors appear to be related to those suspected for SNe Ic. A high kinetic energy, 1052 erg, is also favored. Normal mechanisms of powering core-collapse or thermonuclear SNe do not seem to work for these SNe. We consider models powered by 56Ni decay and interaction with circumstellar material, but we find that the creation and spin-down of a magnetar with a period of 2 ms, a magnetic field of 2 × 1014 G, and a 3 M ⊙ progenitor provides the best fit to the data.