We report ALMA Early Science CO(1-0) and CO(3-2) observations of the brightest cluster galaxy (BCG) in Abell 1664. The BCG contains 1.1x10^{10} solar masses of molecular gas divided roughly equally between two distinct velocity systems: one from -250 to +250 km/s centred on the BCGs systemic velocity and a high velocity system blueshifted by 570 km/s with respect to the systemic velocity. The BCGs systemic component shows a smooth velocity gradient across the BCG center with velocity proportional to radius suggestive of solid body rotation about the nucleus. However, the mass and velocity structure are highly asymmetric and there is little star formation coincident with a putative disk. It may be an inflow of gas that will settle into a disk over several 10^8 yr. The high velocity system consists of two gas clumps, each ~2 kpc across, located to the north and southeast of the nucleus. Each has a line of sight velocity spread of 250-300 km/s. The velocity of the gas in the high velocity system tends to increase towards the BCG center and could signify a massive high velocity flow onto the nucleus. However, the velocity gradient is not smooth and these structures are also coincident with low optical-UV surface brightness regions, which could indicate dust extinction associated with each clump. If so, the high velocity gas would be projected in front of the BCG and moving toward us along the line of sight in a massive outflow most likely driven by the AGN. A merger origin is unlikely but cannot be ruled out.
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