We report the results of near-infrared Very Large Telescope (VLT)-Infrared Spectrometer and Array Camera (ISAAC) spectroscopy of a sample of 12 galaxies at z=0.4-1.4, drawn from the ISOCAM survey of the Hubble Deep Field South. We find that the rest-frame R-band spectra of the ISOCAM galaxies resemble those of powerful dust-enshrouded starbursts. Hα emission is detected in 11 out of 12 objects down to a flux limit of 7×10-17 ergs cm-2 s-1, corresponding to a luminosity limit of 1041 ergs s-1 at z=0.6 (for an H0=50 and Ω=0.3 cosmology). From the Hα luminosities in these galaxies we derive estimates of the star formation rate (SFR) in the range 2-50 Msolar yr-1 for stellar masses 1-100 Msolar. The raw Hα-based SFRs are an order of magnitude or more lower than SFR (far-infrared) estimates based on ISOCAM LW3 fluxes. If the Hα emission is corrected for extinction, the median offset is reduced to a factor of 3. The sample galaxies are part of a new population of optically faint but infrared-luminous active starburst galaxies, which are characterized by an extremely high rate of evolution with redshift up to z~1.5 and are expected to contribute significantly to the cosmic far-infrared extragalactic background. Based on observations with ISO, an ESA project with instruments funded by ESA member states (especially the PI countries: France, Germany, the Netherlands, and the United Kingdom) with the participation of the Institute of Space and Astronautical Science and NASA.