We present the discovery of WASP-39b, a highly inflated transiting Saturn-mass planet orbiting a late G-type dwarf star with a period of $4.055259 pm 0.000008$,d, Transit Epoch T$_{0}=2455342.9688pm0.0002$,(HJD), of duration $0.1168 pm 0.0008$,d. A combined analysis of the WASP photometry, high-precision follow-up transit photometry, and radial velocities yield a planetary mass of $mpl=0.28pm0.03,mj$ and a radius of $rpl=1.27pm0.04,rj$, resulting in a mean density of $0.14 pm 0.02,rhoj$. The stellar parameters are mass $mstar = 0.93 pm 0.03,msun$, radius $rstar = 0.895pm 0.23,rsun$, and age $9^{+3}_{-4}$,Gyr. Only WASP-17b and WASP-31b have lower densities than WASP-39b, although they are slightly more massive and highly irradiated planets. From our spectral analysis, the metallicity of WASP-39 is measured to be feh,$= -0.12pm0.1$,dex, and we find the planet to have an equilibrium temperature of $1116^{+33}_{-32}$,K,. Both values strengthen the observed empirical correlation between these parameters and the planetary radius for the known transiting Saturn-mass planets.
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