ABSTRACT Several evidences indicate that Lyman Break Galaxies (LBGs) in the Epoch of Reionization (redshift z > 6) might host massive black holes (MBHs). 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 MUV = −22 residing in an Mh ≈ 1012 M⊙ halo at z = 6 host an MBH with mass M• ≈ 2 × 108 M⊙. Depending on the fraction, fseed, of early haloes planted with a direct collapse black hole seed (Mseed = 105M⊙), the model suggests two possible scenarios: (i) if fseed = 1, MBHs in LBGs mostly grow by merging and must accrete at a low (λE ≃ 10−3) Eddington ratio not to exceed the experimental X-ray luminosity upper bound $L_\mathrm{ X}^* = 10^{42.5} {\rm erg\, s}^{-1}$; (ii) if fseed = 0.05, accretion dominates (λE ≃ 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, $M_{\rm UV} \lower.5ex\hbox{$\,\, \buildrel\gt \over \sim \,\,$}-23$, with BH emission playing a subdominant role. Scenario (i) poses extremely challenging, and possibly unphysical, requirements on DCBH formation. Scenario (ii) entails testable implications on the physical properties of LBGs involving the FIR luminosity, emission lines, and the presence of outflows.