The optical region of a number of reddened O-type stars has been examined on Keck I HIRES spectrograms (R = 45,000) for evidence of interstellar C(60). No absorption features were detected near the laboratory C(60) wavelengths 3857 and 3980 Angstrom. An interstellar feature is present at 6220.8 Angstrom, but it is unacceptably far from the laboratory gas-phase wavelength of 6217.5 Angstrom. It is probably just another of the weak diffuse interstellar bands (DIBs), which are numerous in that spectral region. The most astronomically promising C(60) feature was measured in the laboratory at 3284 Angstrom in liquid or solid matrices. Its gas-phase wavelength can be inferred either from matrix shifts of C(60) features at longer wavelengths or from high-temperature gas-phase measurements. On that evidence, the interstellar feature could fall anywhere between about 3244 and 3306 Angstrom. Its width is uncertain but here is taken to be about 1 Angstrom. No interstellar absorption fitting these specifications and as strong as 16 m Angstrom has been detected in the stars observed, including Cyg OB2/8A of E(B-V) = 1.60. It follows that in that particular line of sight and for the assumed FWHM of 1 Angstrom, N(C(60)) < 4.5 x 10(11) cm(-2). However, some recent laboratory spectroscopy suggests that its width may be very much larger, in which case this limit would be invalid. At this upper limit, the corresponding number of carbon atoms contained in neutral C(60) indicates that that molecule would be only a minor contributor to the total amount of C in that direction, and would be less than 1% of the amount that may be tied up in the DIBs. Stronger C(60), bands are known in the laboratory at approximately 2110 and 2566 <Angstrom> but the upper limit on 3284 Angstrom suggests that they will not be easy to detect without high resolution, high signal-to-noise ratio (S/N) satellite spectroscopy and better laboratory gas-phase wavelengths. An estimate of the column density of C(60)(+), under the assumption that the 9577, 9632 Angstrom bands are indeed due to C(60)(+) and that the laboratory f-value is correct, indicates that the C(60)(+)/C(60) abundance in that line of sight is greater than 100.