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The twist angle constitutes an important control knob in twisted bilayer graphene and related moiré materials that has become accessible in-situ. It effectively tunes between weakly interacting and strongly correlated electrons. We propose that this facilitates the realisation of a chiral phase transition in moiré Dirac materials. We argue that the transition in twisted bilayer graphene can be described by the Gross-Neveu-Yukawa model that couples Dirac fermions and an XY order parameter field. The quantum critical behavior of this effective model is consistent with quantum Monte Carlo simulations of the continuum model for twisted bilayer graphene. We also study finite-temperature effects above the corresponding relativistic quantum critical point and reveal regimes of quantum criticality, precondensation, and a "non-Dirac liquid”.