We have measured X((3)) for a series of solid-state samples of polyphenylene oligomers, (Ph)(n), where n = 4-8 is the number of phenyl ring units, using optical pulses of 140 fs duration and 650 nm wavelength. A degenerate four-wave mixing (DFWM) signal was only observable for n equal to or greater than 6, and thereafter the measured values of X((3)) increased monotonically with n. Measurements of the linear absorption are also reported. Although the DFWM measurements were performed at wavelengths far from resonance, the figure of merit X((3))/alpha was essentially flat beyond n equal to or less than 6. In contrast to previous studies of oligomers in solution, the principal nonlinear responses were instantaneous within the 140 fs temporal resolution.