We present initial results and source lists of variable sources in the Large Magellanic Cloud (LMC) for which we detect thermal infrared variability from the Surveying the Agents of a Galaxy's Evolution (SAGE) survey, which had two epochs of photometry separated by 3 months. The SAGE survey mapped a 7° × 7° region of the LMC using the Infrared Array Camera (IRAC) and the MIPS instruments on board Spitzer. Variable sources are identified using a combination of the IRAC 3.6, 4.5, 5.8, 8.0 μ bands and the MIPS 24 μ bands. An error-weighted flux difference between the two epochs is used to assess the variability. Of the ~3 million sources detected at both epochs, we find ~2000 variable sources for which we provide electronic catalogs. Most of the variable sources can be classified as asymptotic giant branch (AGB) stars. A large fraction (>66%) of the extreme AGB stars are variable and only smaller fractions of carbon-rich (6.1%) and oxygen-rich (2.0%) stars are detected as variable sources. We also detect a population of variable young stellar object candidates.