Chaotic cold accretion (CCA) profoundly differs from classic black hole accretion models. Using 3D high-resolution simulations, we probe the impact of rotation on the hot and cold accretion flow in a typical massive galaxy. In the hot mode, with or without turbulence, the pressure-dominated flow forms a geometrically thick rotational barrier, suppressing the accretion rate to ~1/3 of the Bondi rate. When radiative cooling is dominant, the gas loses pressure support and quickly circularizes in a cold thin disk. In the more common state of a turbulent and heated atmosphere, CCA drives the dynamics if the gas velocity dispersion exceeds the rotational velocity, i.e., turbulent Taylor number < 1. Extended multiphase filaments condense out of the hot phase via thermal instability and rain toward the black hole, boosting the accretion rate up to 100 times the Bondi rate. Initially, turbulence broadens the angular momentum distribution of the hot gas, allowing the cold phase to condense with prograde or retrograde motion. Subsequent chaotic collisions between the cold filaments, clouds, and a clumpy variable torus promote the cancellation of angular momentum, leading to high accretion rates. The simulated sub-Eddington accretion rates cover the range inferred from AGN cavity observations. CCA predicts inner flat X-ray temperature and r^{−1} density profiles, as recently discovered in M 87 and NGC 3115. The synthetic H{α} images reproduce the main features of cold gas observations in massive ellipticals, as the line fluxes and the filaments versus disk morphology. Such dichotomy is key for the long-term AGN feedback cycle. As gas cools, filamentary CCA develops and boosts AGN heating; the cold mode is thus reduced and the rotating disk remains the sole cold structure. Its consumption leaves the atmosphere in hot mode with suppressed accretion and feedback, reloading the cycle.