  We predict the existence and observational signatures of a new class of
objects that assembled early, during the first billion years of cosmic time:
Obese Black-hole Galaxies (OBGs). OBGs are objects in which the mass of the
central black hole initially exceeds that of the stellar component of the host
galaxy, and the luminosity from black-hole accretion dominates the starlight.
From a cosmological simulation, we demonstrate that there are sites where star
formation is initially inhibited and direct-collapse black holes (DCBHs) form
due to the photo-dissociating effect of Lyman-Werner radiation on molecular
hydrogen. We show that the formation of OBGs is inevitable, because the
probability of finding the required extra-galactic environment and the right
physical conditions in a halo conducive to DCBH formation is quite high in the
early universe. We estimate an OBG number density of 0.009/Mpc^3 at z~8 and
0.03/Mpc^3 at z~6. Extrapolating from our simulation volume, we infer that the
most luminous quasars detected at z~6 likely transited through an earlier OBG
phase. We find that these primordial galaxies start off with an over-massive BH
and acquire their stellar component from subsequent merging as well as in-situ
star formation. In doing so, they inevitably go through an OBG phase dominated
by the accretion luminosity at the Eddington rate or below, released from the
growing BH. The OBG phase is characterised by an ultra-violet (UV) spectrum
with slope of beta ~ -2.3 and the absence of a Balmer Break. OBGs should also
be spatially unresolved, and are expected to be brighter than the majority of
known high-redshift galaxies. OBGs could potentially be revealed via HST
follow-up imaging of samples of brighter Lyman-break galaxies provided by
wide-area ground-based surveys such as UltraVISTA, and should be easily
uncovered and studied with instruments aboard JWST...(abridged)
