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We present the first results from the HST Archival Legacy project "SKYSURF." As described in Windhorst et al., SKYSURF utilizes the large HST archive to study the diffuse UV, optical, and near-IR backgrounds and foregrounds in detail. Here, we utilize SKYSURF's first sky-surface-brightness measurements to constrain the level of near-IR diffuse Extragalactic Background Light (EBL) in three near-IR filters (F125W, F140W, and F160W). This is done by comparing our preliminary sky measurements of >30,000 images to zodiacal light models, carefully selecting the darkest images to avoid contamination from stray light. Our sky-surface-brightness measurements have been verified to an accuracy of better than 1%, which when combined with systematic errors associated with HST, results in sky-brightness uncertainties of ∼ 2%–4% ≃ 0.005 MJy sr−1 in each image. When compared to the Kelsall et al. zodiacal model, an isotropic diffuse background of ∼30 nW m−2 sr−1 remains, whereas using the Wright zodiacal model results in no discernible diffuse background. Based primarily on uncertainties in the foreground model subtraction, we present limits on the amount of diffuse EBL of 29, 40, and 29 nW m−2 sr−1, for F125W, F140W, and F160W, respectively. While this light is generally isotropic, our modeling at this point does not distinguish between a cosmological origin or a solar system origin (such as a dim, diffuse, spherical cloud of cometary dust).