We present ~1000 new candidate Young Stellar Objects (YSOs) in the Large Magellanic Cloud selected from Spitzer Space Telescope data, as part of the Surveying the Agents of a Galaxy's Evolution (SAGE) Legacy program. The YSOs, detected by their excess infrared (IR) emission, represent early stages of evolution, still surrounded by disks and/or infalling envelopes. Previously, fewer than 20 such YSOs were known. The candidate YSOs were selected from the SAGE Point Source Catalog from regions of color-magnitude space least confused with other IR-bright populations. The YSOs are biased toward intermediate- to high-mass and young evolutionary stages, because these overlap less with galaxies and evolved stars in color-magnitude space. The YSOs are highly correlated spatially with atomic and molecular gas, and are preferentially located in the shells and bubbles created by massive stars inside. They are more clustered than generic point sources, as expected if star formation occurs in filamentary clouds or shells. We applied a more stringent color-magnitude selection to produce a subset of "high-probability" YSO candidates. We fitted the spectral-energy distributions (SEDs) of this subset and derived physical properties for those that were well fitted. The total mass of these well-fitted YSOs is ~2900 M_☉ and the total luminosity is ~2.1 × 10^6 L_☉ . By extrapolating the mass function with a standard initial mass function and integrating, we calculate a current star-formation rate of ~0.06 M_☉ yr^(–1), which is at the low end of estimates based on total ultraviolet and IR flux from the galaxy (~0.05 – 0.25 M_☉ yr^(–1)), consistent with the expectation that our current YSO list is incomplete. Follow-up spectroscopy and further data mining will better separate the different IR-bright populations and likely increase the estimated number of YSOs. The full YSO list is available as electronic tables, and the SEDs are available as an electronic figure for further use by the scientific community.