We present a Parkes multibeam H i survey of the Large Magellanic Cloud (LMC). This survey, which is sensitive to spatial structure in the range 200 pc to 10 kpc, complements the Australia Telescope Compact survey, which is sensitive to structure in the range 15-500 pc. With an rms column density sensitivity of 8 x 10(16) cm(-2) for narrow lines and 4 x 10(17) cm(-2) for typical linewidths of 40 km s(-1), emission is found to be extensive well beyond the main body of the LMC. Arm-like features extend from the LMC to join the Magellanic Bridge and the Leading Arm, a forward counterpart to the Magellanic Stream. These features, whilst not as dramatic as those in the Small Magellanic Cloud, appear to have a common origin in the Galactic tidal field, in agreement with recent 2MASS and DENIS results for the stellar population. The diffuse gas that surrounds the LMC, particularly at PAs of 90degrees-330degrees, appears to be loosely associated with tidal features, but loosening by the ram pressure of tenuous Galactic halo gas against the outer parts of the LMC cannot be discounted. High-velocity clouds, which lie between the Galaxy and the LMC in velocity and that appear in the ultraviolet spectra of some LMC stars, are found to be associated with the LMC if their heliocentric velocity exceeds approximately +100 km s(-1) . They are possibly the product of energetic outflows from the LMC disc. The H i mass of the LMC is found to be (4.8 +/- 0.2) x 10(8) M-circle dot (for an assumed distance of 50 kpc), substantially more than previous recent measurements.