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Once the number of massless fermions exceeds a critical value $N_f^*$, many-flavour QCD enters the conformal window, where chiral symmetry remains intact in the vacuum. In lattice simulations the theory can only be probed at a finite cutoff, finite temporal extent and nonzero quark mass. The latter invariably breaks chiral symmetry and thus one generically observes a thermal chiral transition also for $N_f\geq N_f^*$. For QCD to correspond to an infrared conformal theory, this transition must not be connected to the continuum chiral limit. In this work, we present the chiral phase boundaries of unimproved staggered fermions in the bare lattice parameter space $(N_\tau,\, \beta,\, am,\, N_f)$, focusing on a direct comparison between $N_f=7$ and $N_f=8$. For $N_f=7$, we find that the chiral transition remains present in the continuum chiral limit $(\beta\to\infty, \, N_\tau\to\infty, \, am\to0)$. For $N_f=8$, by contrast, the transition is absent in this limit; instead, the massless continuum theory is chirally symmetric in the vacuum. This suggests that the conformal window opens at $N_f^*=8$.