We perform a measurement of the tune-out wavelength, λ 0 , between the D 1 , 6 2 S 1/2 → 6 2 P 1/2 , and D 2 , 6 2 S 1/2 → 6 2 P 3/2 , transitions for 133 Cs in the ground hyperfine state (F = 3, m F = +3). At λ 0 , the frequencydependent scalar polarizability is zero leading to a zero scalar ac Stark shift. We measure the polarizability as a function of wavelength using Kapitza-Dirac scattering of a 133 Cs Bose-Einstein condensate in a one-dimensional optical lattice, and determine the tune-out wavelength to be λ 0 = 880.21790( 40) stat (8) sys nm. From this measurement we determine the ratio of reduced matrix elements to be 1.9808(2). This represents an improvement of a factor of 10 over previous results derived from excited-state lifetime measurements. We use the present measurement as a benchmark test of high-precision theory.