We present a 1.1 mm wavelength imaging survey covering 0.3 deg2 in the COSMOS field. These data, obtained with the AzTEC continuum camera on the James Clerk Maxwell Telescope, were centred on a prominent large-scale structure overdensity which includes a rich X-ray cluster at z≈ 0.73. A total of 50 mm-galaxy candidates, with a significance ranging from 3.5 to 8.5σ, are extracted from the central 0.15 deg2 area which has a uniform sensitivity of ∼1.3 mJy beam−1. 16 sources are detected with S/N ≥ 4.5, where the expected false-detection rate is zero, of which a surprisingly large number (9) have intrinsic (deboosted) fluxes ≥5 mJy at 1.1 mm. Assuming the emission is dominated by radiation from dust, heated by a massive population of young, optically obscured stars, then these bright AzTEC sources have far-infrared luminosities >6 × 1012 L⊙ and star formation rates >1100 M⊙ yr−1. Two of these nine bright AzTEC sources are found towards the extreme peripheral region of the X-ray cluster, whilst the remainder are distributed across the larger scale overdensity. We describe the AzTEC data reduction pipeline, the source-extraction algorithm, and the characterization of the source catalogue, including the completeness, flux deboosting correction, false-detection rate and the source positional uncertainty, through an extensive set of Monte Carlo simulations. We conclude with a preliminary comparison, via a stacked analysis, of the overlapping MIPS 24-μm data and radio data with this AzTEC map of the COSMOS field.