We present high spatial resolution CO(1-0) mapping of the luminous infrared galaxy NGC6240 obtained with the IRAM - Plateau de Bure Interferometer. This source is a well-known early-stage merging system hosting two AGN. We find a broad CO(1-0) line profile, with maximum velocity 800 km/s and FWZI=1400 km/s, and displaying several kinematic components, revealing the complexity of the gas dynamics in this system. We detect a blueshifted CO emission with velocity in the range -200 and -500 km/s, peaked around the southern AGN, at the same position where the H2 outflow is located, and with a mass loss rate of ~500 Msun/yr. We interpret this blueshifted component as a outflow, originating from the southern nucleus. The spatial and spectral match strongly suggests that the CO outflow is connected to the H2 superwind located around the southern nucleus, and to the large scale CO outflow, with similar velocities, extended on scales of 10 kpc. The large mass loading factor (dM/dt /SFR ~ 10) of the molecular gas suggests that the outflow is likely driven by both SNa winds and the radiation of the southern AGN. We discovered a nuclear, redshifted CO emission peaking in the mid point of the two nuclei, as it is the case for the CO emission at the systemic velocity. The large velocity dispersion, which reaches its maximum (~500 Km/s) in the mid point between the two nuclei, suggests that the gas might be highly turbulent in this region, although the presence of an unresolved rotation component cannot be ruled out. ; Comment: Accepted for publication in A&A. . 7 pages, 7 figures