We exploit the first data release from the Gaia mission to identify candidate Mira variables in the outskirts of the Magellanic Clouds. The repeated observations of sources during the initial phase of the Gaia mission is used to identify stars that show signs of variability. This variability information, combined with infrared photometry from 2MASS and WISE, allows us to select a clean sample of giants in the periphery of the LMC. We find evidence for Miras surrounding the LMC out to ~20 deg in all directions, apart from the North-West quadrant. Our sample does not generally follow the gas distribution of the Magellanic system; Miras are notably absent in the gaseous bridge between the LMC and SMC, but they are likely related to the stellar RR Lyrae bridge reported by Belokurov et al. (2016). The stellar stream discovered by Mackey et al. (2016) to the North of the LMC is almost perfectly delineated by our Mira variables, and likely extends further East toward the Galactic plane. The presence of an intermediate-age population in this stream advocates an LMC disc origin. We also find a significant excess of Miras to the East of the LMC; these more diffusely distributed stars are likely stripped SMC stars due to interactions with the LMC. Miras are also identified in regions of the sky away from the Clouds; we locate stars likely associated with known massive substructures, and also find potential associations with stripped SMC debris above the Galactic plane.