We report on a global CCD time-series photometric campaign to decode the pulsations of the nucleus of the planetary nebula NGC 1501. The WC4 central star is an extremely hot, hydrogen-deficient, ``OVI''-type object, with some spectroscopic characteristics similar to those of the pre-white-dwarf PG 1159-035 stars. NGC 1501 shows pulsational brightness variations of a few percent with numerous individual periods ranging from 19 to 87 minutes. The pulsation amplitudes and periods are highly variable, suggesting a complex pulsation spectrum that requires a long unbroken time series to resolve. To that end, we obtained CCD photometry of the central star over a two-week period in 1991 November, using a network of observatories around the globe. We obtained nearly continuous coverage over an interval of almost one week in the middle of the run. With this data set, we have identified 10 independent pulsation periods, ranging from 5235~s down to 1154 s. The pulsation modes changed amplitude significantly during the course of the run, indicating either real amplitude variations, or that the modes are not fully resolved over the two-week interval. We find strong evidence that the modes we see in this star are indeed nonradial g-modes. The ratios of the frequencies of the largest-amplitude modes agree closely with those expected for modes that are trapped by a density discontinuity in the outer layers. This conclusion is strengthened by including single-site observations of this star, obtained during previous years, in our analysis. We offer a model for the pulsation spectrum that includes a common period spacing of 22.30 s and a stellar rotation period of 1.17 days; the period spacing allows us to assign a preliminary asteroseismological mass of 0.55 +/- 0.03 Msun. However, several factors complicate the analysis. Aside from the proximity of the rotational splitting to 1 cycle per day, this frequency splitting corresponds closely to period spacings near 20 seconds near the dominant frequencies of the star. Thus, the period spacing and frequency spacings are nearly degenerate.