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We study nuclear quantum effects in H/D sticking to graphene, comparing scattering experiments at near-zero coverage with classical, quantized, and transition-state calculations. The experiment shows H/D sticking probabilities that are indistinguishable from one another and markedly smaller than those expected from a consideration of zero-point energy shifts of the chemisorption transition state. Inclusion of dynamical effects and vibrational anharmonicity via ring-polymer molecular dynamics (RPMD) yields results that are in good agreement with the experimental results. RPMD also reveals that nuclear quantum effects, while modest, arise primarily from carbon and not from H/D motion, confirming the importance of a C atom rehybridization mechanism associated with H/D sticking on graphene.