The first experimental determination of Saturn's J6 is derived from the simultaneous solution of three linear relations involving Saturn's zonal gravity harmonics. Two of these relations arise from the combined analysis of Pioneer 11 Doppler tracking and satellite secular rate data by Null et al. (1981). The third is the result of the analysis of Voyager 1 and 2 observations of the narrow eccentric ringlet at 1.2908 RS by Porco et al. (1984). On the assumption that the eccentricity of the ringlet is forced by the satellite Titan, we redetermine the location of the Titan apsidal resonance to an accuracy of ¿13 km, which in turn provides a strong constraint on Saturn's zonal gravity harmonics. Combining this constraint with the results of Null et al. and adopting a priori values for J8, J10, and J12 based on interior models we obtain new estimates for the first three zonal gravity coefficients: J2=(16,297¿18)¿10-6, J4=(-910¿61)¿10-6, and J6=(107¿50)¿10-6, all normalized to an equatorial reference radius, RS=60,330 km. Linearized about these nominal values, the Titan ringlet constraint alone may be written in the form J2-1.507(J4+910¿10-6)+1.586(J6-107¿10-6)- 1.430(J8+10¿10-6)+1.181(J10-2¿10-6)-0.922 (J12+0.5¿10-6)+0.692J14-0.505J16= (16,297¿12)¿10-6.