In a recent search for unusually red L and T dwarfs, we identified 2MASS J11193254-1137466 as a likely young L7 dwarf and potential member of the TW Hydrae association. We present spectra that confirm the youth of this object. We also measure a radial velocity of 8.5 ± 3.3 km/s that, together with the sky position, proper motion and photometric distance, results in a 92% probability of membership in the TW Hydrae association, with a calibrated field contamination probability of 0.0005% using the BANYAN II tool. Using the age of TW Hydrae and the luminosity of 2MASS J1119-1137, we estimate its mass to be 4.3—7.6 MJup. It is the lowest-mass and nearest isolated member of TW Hydrae at a kinematic distance of 28.9 ± 3.6pc. It is also among the brightest isolated <10 MJup object discovered to date, second only to PSO J318.5-22 and at half the age.