  We present the first results from a near-infrared narrow-band search for
primeval galaxies (PGs) using the Keck 10~m telescope. We have targeted our
fields for three QSOs and one radio galaxy at redshifts $z = 2.28$ to $4.70$.
We selected narrow-band filters in the $K$-band centered on strong emision
lines at the redshift of the targets. We reach limiting fluxes between
$1.6\times 10^{-17}$~erg~s$^{-1}$~cm$^{-2}$ and $1.0\times
10^{-16}$~erg~s$^{-1}$~cm$^{-2}$, and cover a total area of $\sim
4$~arcmin$^2$. At the redshifts of interest, these flux limits correspond to
typical restframe line luminosities of $\sim 10^{42} - 10^{43}$~erg~s$^{-1}$,
unobscured star formation rates of $\sim 1 - 100$ $M_\odot$~yr$^{-1}$, and a
sampled comoving volume of several tens of Mpc$^3$. We have found no candidate
PGs at a $2\sigma$ confidence level. We demonstrate that for moderate dust
absorption ($A_V \gsim 2^m$) in a simple dust-screen model, our preliminary
survey puts a strong constraint on intrinsic PG luminosities during an intial
burst of star formation. In the case of the QSOs, we have used PSF-subtraction
to search for the presence of faint, extended line emission surrounding these
radio-quiet AGNs. We find no evidence for extended emission down to $3.7 \times
10^{-17}$~erg~s$^{-1}$~cm$^{-2}$. This imposes limits on the reprocessed
fraction of the QSO continuum emission ranging between $0.02$\% and $0.29$\%;
if beaming effects are not important, then this implies similarly small
covering factors for clouds optically thick to the QSO continuum emission.
