Recent theories propose that quantum gravity effects may be observable at LEP energies via gravitons that couple to Standard Model particles and propagate into extra spatial dimensions. The associated production of a graviton and a photon is searched for as well as the effects of virtual graviton exchange in the processes: e + e − → γγ , ZZ, W + W − , μ + μ − , τ + τ − , q q ̄ and e + e − . No evidence for this new interaction is found in the data sample collected by the L3 detector at LEP at centre-of-mass energies up to 183 GeV. Limits close to 1 TeV on the scale of this new scenario of quantum gravity are set.