We present a high-resolution (3.6“, 70 pc) CO(1-0) mosaic of the molecular gas in M 82 covering an area of 2.5'x3.5’ (2.8 kpc x 3.9 kpc) obtained with the OVRO millimeter interferometer. The observations reveal the presence of huge amounts of molecular gas (> 70% of the total molecular mass, Mtot ≈ 1.3 × 109M⊙) outside the central 1 kpc disk. Molecular streamers are detected in and below M 82's disk out to distances from the center of ~1.7 kpc. Some of these streamers are well correlated with optical absorption features; they form the basis of some of the prominent tidal HI features around M 82. This provides evidence that the molecular gas within M 82's optical disk is disrupted by the interaction with M 81. Molecular gas is found in M 82's outflow/halo, reaching distances up to 1.2 kpc below the plane; CO line-splitting has been detected for the first time in the outflow. The maximum outflow velocity is ~ 230 km s−1; we derive an opening angle of ~ 55° for the molecular outflow cone. The total amount of gas in the outflow is > 3 × 108 M⊙ and its kinetic energy is of order 1055 erg, about one percent of the estimated total mechanical energy input of M 82's starburst. Our study implies that extreme starburst environments can move significant amounts of molecular gas in to a galaxy's halo (and even to the intergalactic medium).