Using Blue Horizontal Branch stars identified in the Dark Energy Survey Year 1 data, we report the detection of an extended and lumpy stellar debris distribution around the Magellanic Clouds. At the heliocentric distance of the Clouds, overdensities of BHBs are seen to reach at least to ~30 degrees, and perhaps as far as ~50 degrees from the LMC. In 3D, the stellar halo is traceable to between 25 and 50 kpc from the LMC. We catalogue the most significant of the stellar sub-structures revealed, and announce the discovery of a number of narrow streams and diffuse debris clouds. Two narrow streams appear approximately aligned with the Magellanic Clouds' proper motion. Moreover, one of these overlaps with the gaseous Magellanic Stream on the sky. Curiously, two diffuse BHB agglomerations seem coincident with several of the recently discovered DES satellites. Given the enormous size and the conspicuous lumpiness of the LMC's stellar halo, we speculate that the dwarf could easily have been more massive than previously had been assumed.