Recently, Haldane proposed a new geometric description for the fractional quantum Hall (FQH) effect, suggesting the existence of a previously overlooked quantum metric. Novel collective excitations called chiral graviton modes (CGMs) are proposed as quanta of the metric fluctuations. Such modes are condensed-matter analogues of gravitons that are hypothetical spin-2 bosons, and could be described by the corresponding Fierz-Pauli field equations in FQH liquids. CGMs are characterized by polarized states with chirality of +2 or -2, and energy gaps coinciding with fundamental neutral collective excitations (i.e., magnetorotons) in the long-wavelength limit. However, CGMs remain experimentally inaccessible. Here, we observe chiral graviton modes in FQH liquids using inelastic scattering of circularly-polarized light. The experiments are performed in a GaAs quantum well. At filling factor v = 1/3, the long-wavelength magnetoroton emerges under a specific polarization scheme corresponding to angular momentum -2. Remarkably, the mode chirality remains -2 at v = 2/5 but becomes the opposite at v = 2/3 and 3/5. The observations capture the essentials of the graviton modes and support the new FQH geometrical description. Our work offers access to quantum gravity physics in bench-top experiments.