  We show that a non-commutative structure arises naturally from perturbative
quantum gravity in a de Sitter background metric. Our work builds on recent
advances in the construction of observables in highly symmetric background
spacetimes [Brunetti et al., JHEP 08, 032 (2016); Fr\"ob and Lima, Class.
Quant. Grav. 35, 095010 (2018)], where the dynamical coordinates that are
needed in the relational approach were established for such backgrounds to all
orders in perturbation theory. We show that these dynamical coordinates that
describe events in the perturbed spacetime are naturally non-commuting, and
determine their commutator to leading order in the Planck length. Our result
generalizes the causal non-commutative structure that was found using the same
approach in Minkowski space [Fr\"ob, Much and Papadopoulos, Phys. Rev. D 107,
064041 (2023)].
