Broad-band optical observations of the extraordinarily bright optical afterglow of the intense gamma-ray burst GRB 991208 started ~2.1 days after the event and continued until 4 Apr. 2000. The flux decay constant of the optical afterglow in the R-band is -2.30 +/- 0.07 up to ~5 days, which is very likely due to the jet effect, and it is followed by a much steeper decay with constant -3.2 +/- 0.2, the fastest one ever seen in a GRB optical afterglow. A negative detection in several all-sky films taken simultaneously with the event, that otherwise would have reached naked eye brightness, implies either a previous additional break prior to ~2 days after the occurrence of the GRB (as expected from the jet effect) or a maximum, as observed in GRB 970508. The existence of a second break might indicate a steepening in the electron spectrum or the superposition of two events, resembling GRB 000301C. Once the afterglow emission vanished, contribution of a bright underlying supernova was found on the basis of the late-time R-band measurements, but the light curve is not sufficiently well sampled to rule out a dust echo explanation. Our redshift determination of z = 0.706 indicates that GRB 991208 is at 3.7 Gpc (for Ho = 60 km s-1 Mpc-1, OMEGAo = 1 and LAMDAo = 0), implying an isotropic energy release of 1.15 x 1053 erg which may be relaxed by beaming by a factor >102. Precise astrometry indicates that the GRB coincides within 0.2" with the host galaxy, thus supporting a massive star origin. The absolute magnitude of the galaxy is MB = -18.2, well below the knee of the galaxy luminosity function and we derive a star-forming rate of (11.5 +/- 7.1) Msun yr-1, which is much larger than the present-day rate in our Galaxy. The quasi-simultaneous broad-band photometric spectral energy distribution of the afterglow was determined ~3.5 day after the burst (Dec. 12.0) implying a cooling frequency nuc below the optical band, i.e. supporting a jet model with p = -2.30 as the index of the power-law electron distribution.