Making use of the multiplexing facilities of the Gemini Multi-Object Spectrograph, we were able to investigate the presence of binary stars within the ionizing cluster of 30 Doradus. From a seven-epoch observing campaign at Gemini South we detect a binary candidate rate of about 50%, which is consistent with an intrinsic 100% binary rate among massive stars. We find that single-epoch determinations of the velocity dispersion give values around 30 km s^–1. After correcting the global velocity dispersion for the binary orbital motions, the "true" cluster velocity dispersion is 8.3 km s^–1. This value implies a virial mass of about 8% of the mass calculated using the single-epoch value. The binary corrected virial mass estimate is consistent with photometric mass determinations, thus suggesting that NGC 2070 is a firm candidate for a future globular cluster.