  The study of the extragalactic background light (EBL) in the optical and near
infrared has received a lot of attention in the last decade, especially near a
wavelength of $\lambda\approx 3.4\operatorname{\mu m}$, with remaining tension
among different techniques for estimating the background. In this paper we
present a measurement of the contribution of galaxies to the EBL at
$3.4\operatorname{\mu m}$ that is based on the measurement of the luminosity
function (LF) in Lake et al. (2018) and the mean spectral energy distribution
of galaxies in Lake & Wright (2016). The mean and standard deviation of our
most reliable Bayesian posterior chain gives a $3.4\operatorname{\mu m}$
background of $I_\nu = 9.0\pm0.5 \operatorname{kJy} \operatorname{sr}^{-1}$
($\nu I_\nu = 8.0\pm0.4 \operatorname{nW} \operatorname{m}^{-2}
\operatorname{sr}^{-1} e\operatorname{-fold}^{-1}$), with systematic
uncertainties unlikely to be greater than $2\operatorname{kJy}
\operatorname{sr}^{-1}$. This result is higher than most previous efforts to
measure the contribution of galaxies to the $3.4\operatorname{\mu m}$ EBL, but
is consistent with the upper limits placed by blazars and the most recent
direct measurements of the total $3.4\operatorname{\mu m}$ EBL.
