Polyynes represent a unique class of conjugated organic compounds. The third-order nonlinear optical response of polyynes has been extensively modeled theoretically, and it is generally believed that the increase in molecular second hyperpolarizability (gamma) as a function of length for polyynes should be lower than that for polyenes. Experimental evidence to test this prediction, however, has been absent. We have synthesized conjugated polyynes that contain up to 20 consecutive sp-hybridized carbons, and we have determined their nonresonant gamma-values as a function of the number of acetylene repeat units (n). These gamma-values demonstrate a power-law behavior versus n(gammasimilar ton(4.28+/-0.13)), with an exponent that is both larger than theoretically predicted for polyynes and substantially higher than that observed for polyenes or polyenynes. Furthermore, no saturation of the linear or nonlinear optical properties is observed. (C) 2004 American Institute of Physics.