Context : Among the intermediate mass , magnetic chemically peculiar ( MCP ) stars , CU Vir is one of the most intriguing objects . Its 100 % circularly polarized beams of radio emission sweep the Earth as the star rotates , thus making this strongly magnetic star the prototype of a class of non degenerate stellar radio pulsars . While CU Vir is well studied in radio , its high-energy properties are not known . Yet , X-ray emission is expected from stellar magnetospheres and confined stellar winds . Aims : Using X-ray data we aim to test CU Vir for intrinsic X-ray emission and investigate mechanisms responsible for its generation . Methods : We present X-ray observations performed with XMM-Newton and Chandra and study obtained X-ray images , light curves and spectra . Basic X-ray properties are derived from spectral modelling and are compared with model predictions . In this context we investigate potential thermal and non-thermal X-ray emission scenarios . Results : We detect an X-ray source at the position of CU Vir . With L _ { X } \approx 3 \times 10 ^ { 28 } erg s ^ { -1 } it is moderately X-ray bright , but the spectrum is extremely hard compared to other Ap stars . Spectral modelling requires multi-component models with predominant hot plasma at temperatures of about T _ { X } = 25 MK or , alternatively , a nonthermal spectral component . Both types of model provide a virtually equivalent description of the X-ray spectra . The Chandra observations was performed six years later than the one by XMM-Newton , yet the source has similar X-ray flux and spectrum , suggesting a steady and persistent X-ray emission . This is further confirmed by the X-ray light curves that show only mild X-ray variability . Conclusions : CU Vir is also at X-ray energies an exceptional star . To explain its full X-ray properties , a generating mechanism beyond standard explanations like the presence of a low-mass companion or magnetically confined wind-shocks is required . Magnetospheric activity might be present or , as proposed for fast rotating strongly magnetic Bp stars , the X-ray emission of CU Vir is predominantly auroral in nature .