We have measured the absolute optical frequency of the cesium D-1 line at 335 THz (895 nm). This frequency provides an important link for a new determination of the fine structure constant alpha. The D-1 line has been compared with the fourth harmonic of a methane stabilized He-Ne laser at 88.4 THz (3.39 mu m). To measure the frequency mismatch of 18.39 THz between 4 x 88.4 THz = 354 THz and the D-1 line a frequency comb spanning around 244000 modes of a Kerr-lens mode-locked laser was used. We find 1167688 (81) kHz for the hyperfine splitting of the 6P(1/2) State and 335 116 048 807 (41) kHz for the hyperfine centroid from which we derive alpha(-1) = 137.0359924(41). [S0031-9007(99)09057-2].