  We present the first results from the HST Archival Legacy project "SKYSURF."
As described in Windhorst et al. 2022, 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).
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 $\sim$2-4% $\simeq$ 0.005 MJy/sr in
each image. We put limits on the amount of diffuse EBL in three near-IR filters
(F125W, F140W, and F160W) 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. In addition, we investigate the impact
that instrumental thermal emission has on our measurements, finding that it has
a limited impact on F125W and F140W measurements, whereas uncertainties in the
exact thermal state of HST results in significant uncertainties in the level of
astrophysical diffuse light in F160W images. When compared to the Kelsall et
al. (1998) Zodiacal model, an isotropic diffuse background of $30$ nW m$^{-2}$
sr$^{-1}$ remains, whereas using the Wright (1998) 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 nW m$^{-2}$ sr$^{-1}$, 40 nW m$^{-2}$ sr$^{-1}$, 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).
