  In the Hubble Deep Field (HDF), twelve candidate sources of high-redshift (z
> 3.5) AGN activity have been identified. The color selection criteria were
established by passing spectra of selected quasars and Seyfert galaxies
(appropriately redshifted and modified for "Lyman forest" absorption), as well
as stars, observed normal and starburst galaxies, and galaxy models for various
redshifts through the filters used for the HDF observations. The actual
identification of AGN candidates also involved convolving a
Laplacian-of-Gaussian filter with the HDF images, thereby removing relatively
flat galactic backgrounds and leaving only the point-like components in the
centers. Along with positions and colors, estimated redshifts and absolute
magnitudes are reported, with the candidates falling toward the faint end of
the AGN luminosity function. One candidate has been previously observed
spectroscopically, with a measured redshift of 4.02. The number of sources
reported here is consistent with a simple extrapolation of the observed quasar
luminosity function to magnitude 30 in B_Johnson. Implications for ionization
of the intergalactic medium and for gravitational lensing are discussed.
