  CR7 is the brightest Lyman-$\alpha$ emitter observed at $z>6$, which shows
very strong Lyman-$\alpha$ and HeII 1640\AA\ line luminosities, but no metal
line emission. Previous studies suggest that CR7 hosts either young primordial
stars with a total stellar mass of $\sim 10^7\,\mathrm{M}_\odot$ or a black
hole of $\gtrsim 10^6\,\mathrm{M}_\odot$. Here, we explore different formation
scenarios for CR7 with a semianalytical model, based on the random sampling of
dark matter merger trees. We are unable to reproduce the observational
constraints with a primordial stellar source, given our model assumptions, due
to the short stellar lifetimes and the early metal enrichment. Black holes that
are the remnants of the first stars are either not massive enough, or reside in
metal-polluted haloes, ruling out this possible explanation of CR7. Our models
instead suggest that direct collapse black holes, which form in metal-free
haloes exposed to large Lyman-Werner fluxes, are more likely the origin of CR7.
However, this result is derived under optimistic assumptions and future
observations are necessary to further constrain the nature of CR7.
