Context. The asteroseismic exploitation of long period, g-mode hot B subdwarf (sdB) pulsators has been a long sought objective undermined, thus far, by the difficulty of obtaining sufficiently precise and continuous time series data from the ground. Aims: Fast photometry from space appears to be the only means of gathering the appropriate asteroseismic data for this type of star. We explore this possibility with the CoRoT (COnvection, ROtation, and planetary Transits) satellite. Methods: We obtained ~24 days of high quality, nearly continuous photometric data with CoRoT during a short run (SRa03) dedicated to the long period sdB pulsator KPD 0629-0016. We analysed the frequency (period) content of the CoRoT time series by combining Fourier analysis, nonlinear least squares fitting, and prewhitening techniques. Results: Our study has led to the detection of a large number of g-mode pulsations in KPD 0629-0016, with 17 frequencies clearly identified in addition to 7 possible (although more uncertain) peaks emerging above the mean noise level (estimated at ~57 ppm). This is more than is typically detected for sdB stars from the ground and, more importantly, the frequencies of all uncovered g-modes are, for the first time, reliably measured. This paves the way for a detailed asteroseismic analysis of this star. The oscillations are found in the 90-400 muHz frequency range with a dominant mode at 205.29 muHz (P = 1.353 h) of amplitude 0.246% of the mean brightness, i.e., typical of mid-radial order g-mode pulsations. Conclusions: These photometric observations of KPD 0629-0016 demonstrate that g-mode sdB pulsators have rich oscillation spectra that are accessible to current space-based facilities. CoRoT opens up a new era in asteroseismology of hot B subdwarf stars.