Using HST-COS FUV spectra, we have discovered warm molecular hydrogen in the TWA 7 system. TWA 7, a $sim$9 Myr old M2.5 star, has a cold debris disk and has previously shown no signs of accretion. Molecular hydrogen is expected to be extremely rare in a debris disk. While molecular hydrogen can be produced in star spots or the lower chromospheres of cool stars such as TWA 7, fluxes from progressions that get pumped by the wings of Ly$alpha$ indicate that this molecular hydrogen could be circumstellar and thus that TWA 7 is accreting at very low levels and may retain a reservoir of gas in the near circumstellar environment.