We report the results of high-speed optical white-light photometry of the black hole candidate GX 339-4, obtained at the Cerro Tololo Inter-American Observatory during 1996 April. We searched the data for strictly periodic features, quasi-periodic oscillations (QPOs), and aperiodic variability (noise) using Fourier and wavelet techniques. (1) We found a QPO with amplitude 4.5%-6%, frequency f ~ 0.064 Hz, and width Δf/f ~ 0.3-0.5. The QPO was long-lived in that it was present in all segments of the data, even in sets acquired one day apart. (2) In addition to the 0.064 Hz QPO there are indications of low-amplitude QPOs at f = 0.02, 0.03, 0.08, 0.3, and 3 Hz. None of the features appeared in more than one day of data (except for the 0.08 Hz feature) and none of the features were as strong as the 0.064 Hz QPO, and so they should be taken with some caution. (3) We found power in excess of counting statistics out to frequencies of several hertz on both nights. The origin of this excess power is not clear.
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