We present the detection of very extended stellar populations around the Large Magellanic Cloud (LMC) out to R ∼ 21°, or ∼18.5 kpc at the LMC distance of 50 kpc, as detected in the Survey of the Magellanic Stellar History (SMASH) performed with the Dark Energy Camera on the NOAO Blanco 4 m Telescope. The deep (g ∼ 24) SMASH color-magnitude diagrams (CMDs) clearly reveal old (∼9 Gyr), metal-poor (Fe/H −0.8 dex) main-sequence stars at a distance of ∼50 kpc. The surface brightness of these detections is extremely low with our most distant detection at g 34 mag arcsec−2. The SMASH radial density profile breaks from the inner LMC exponential decline at ∼13°-15° and a second component at larger radii has a shallower slope with power-law index = −2.2 that contributes ∼0.4% of the LMC's total stellar mass. In addition, the SMASH densities exhibit large scatter around our best-fit model of ∼70% indicating that the envelope of stellar material in the LMC periphery is highly disturbed. We also use data from the NOAO Source catalog to map the LMC main-sequence populations at intermediate radii and detect a steep dropoff in density on the eastern side of the LMC (at R 8°) as well as an extended structure to the far northeast. These combined results confirm the existence of a very extended, low-density envelope of stellar material with a disturbed shape around the LMC. The exact origin of this structure remains unclear, but the leading options include an accreted halo or tidally stripped outer disk material.