The HERschel Inventory of The Agents of Galaxy Evolution (HERITAGE) of the Magellanic Clouds will use dust emission to investigate the life cycle of matter in both the Large and Small Magellanic Clouds (LMC and SMC). Using the Herschel Space Observatory's PACS and SPIRE photometry cameras, we imaged a 2x8 square degree strip through the LMC, at a position angle of ~22.5 degrees as part of the science demonstration phase of the Herschel mission. We present the data in all 5 Herschel bands: PACS 100 and 160 {μ}m and SPIRE 250, 350 and 500 {μ}m. We present two dust models that both adequately fit the spectral energy distribution for the entire strip and both reveal that the SPIRE 500 {μ}m emission is in excess of the models by 6 to 17%. The SPIRE emission follows the distribution of the dust mass, which is derived from the model. The PAH-to-dust mass (f_PAH) image of the strip reveals a possible enhancement in the LMC bar in agreement with previous work. We compare the gas mass distribution derived from the HI 21 cm and CO J=1-0 line emission maps to the dust mass map from the models and derive gas-to-dust mass ratios (GDRs). The dust model, which uses the standard graphite and silicate optical properties for Galactic dust, has a very low GDR = 65(+15,-18) making it an unrealistic dust model for the LMC. Our second dust model, which uses amorphous carbon instead of graphite, has a flatter emissivity index in the submillimeter and results in a GDR = 287(+25,-42) that is more consistent with a GDR inferred from extinction. ; Comment: To be published in Astronomy & Astrophysics, Herschel First Results Issue