We present near-UV transmission spectroscopy of the highly irradiated transiting exoplanet WASP-12b , obtained with the Cosmic Origins Spectrograph ( COS ) on the Hubble Space Telescope ( HST ) . The spectra cover three distinct wavelength ranges : NUVA ( 2539–2580 Å ) ; NUVB ( 2655–2696 Å ) ; and NUVC ( 2770–2811 Å ) . Three independent methods all reveal enhanced transit depths attributable to absorption by resonance lines of metals in the exosphere of WASP-12b . Light curves of total counts in the NUVA and NUVC wavelength ranges show a detection at a 2.5 \sigma level . We detect extra absorption in the Mg ii \lambda \lambda 2800 resonance line cores at the 2.8 \sigma level . The NUVA , NUVB and NUVC light curves imply effective radii of 2.69 \pm 0.24 R _ { J } , 2.18 \pm 0.18 R _ { J } , and 2.66 \pm 0.22 R _ { J } respectively , suggesting the planet is surrounded by an absorbing cloud which overfills the Roche lobe . We detect enhanced transit depths at the wavelengths of resonance lines of neutral sodium , tin and manganese , and at singly ionised ytterbium , scandium , manganese , aluminum , vanadium and magnesium . We also find the statistically expected number of anomalous transit depths at wavelengths not associated with any known resonance line . Our data are limited by photon noise , but taken as a whole the results are strong evidence for an extended absorbing exosphere surrounding the planet . The NUVA data exhibits an early ingress , contrary to model expectations ; we speculate this could be due to the presence of a disk of previously stripped material .