The discovery of a population of superluminous supernovae (SLSNe), with peak luminosities a factor of similar to 100 brighter than normal supernovae (SNe; typically SLSNe have M-V < -21), has shown an unexpected diversity in core-collapse SN properties. Numerous models have been postulated for the nature of these events, including a strong interaction of the shockwave with a dense circumstellar environment, a re-energizing of the outflow via a central engine, or an origin in the catastrophic destruction of the star following a loss of pressure due to pair production in an extremely massive stellar core (so-called pair instability SNe). Here we consider constraints that can be placed on the explosion mechanism of hydrogen-poor SLSNe (SLSNe-I) via X-ray observations, with XMM-Newton, Chandra, and Swift, and show that at least one SLSN-I is likely the brightest X-ray SN ever observed, with L-X similar to 10(45) erg s(-1), similar to 150 days after its initial discovery. This is a luminosity three orders of magnitude higher than seen in other X-ray SNe powered via circumstellar interactions. Such high X-ray luminosities are sufficient to ionize the ejecta and markedly reduce the optical depth, making it possible to see deep into the ejecta and any source of emission that resides there. Alternatively, an engine could have powered a moderately relativistic jet external to the ejecta, similar to those seen in gamma-ray bursts. If the detection of X-rays does require an engine it implies that these SNe do create compact objects, and that the stars are not completely destroyed in a pair instability event. Future observations will determine which, if any, of these mechanisms are at play in SLSNe.