  Several evidences indicate that Lyman Break Galaxies (LBG) in the Epoch of
Reionization (redshift $z>6$) might host massive black holes (MBH). We address
this question by using a merger-tree model combined with tight constraints from
the 7 Ms Chandra survey, and the known high-$z$ super-MBH population. We find
that a typical LBG with $M_{\rm UV}=-22$ residing in a $M_h\approx 10^{12}
M_\odot$ halo at $z=6$ host a MBH with mass $M_\bullet \approx 2\times 10^8
M_\odot$. Depending on the fraction, $f_{\rm seed}$, of early halos planted
with a direct collapse black hole seed ($M_{\rm seed}=10^5 M_\odot$), the model
suggests two possible scenarios: (a) if $f_{\rm seed}=1$, MBH in LBGs mostly
grow by merging, and must accrete at a low ($\lambda_E\simeq 10^{-3}$)
Eddington ratio not to exceed the experimental X-ray luminosity upper bound
$L_X^* = 10^{42.5} {\rm erg\, s}^{-1}$; (b) if $f_{\rm seed}=0.05$ accretion
dominates ($\lambda_E\simeq 0.22$), and MBH emission in LBGs must be heavily
obscured. In both scenarios the UV luminosity function is largely dominated by
stellar emission up to very bright mag, $M_{\rm UV} > -23$, with BH emission
playing a subdominant role. Scenario (a) poses extremely challenging, and
possibly unphysical, requirements on DCBH formation. Scenario (b) entails
testable implications on the physical properties of LBGs involving the FIR
luminosity, emission lines, and presence of outflows.
