The results of a first search for CP violation in the production and decay of top quark-antiquark ( (t\overline{t}) ) pairs are presented. The search is based on asymmetries in T-odd, triple-product correlation observables, where T is the time-reversal operator. The analysis uses a sample of proton-proton collisions at (\sqrt{s})=8TeV collected by the CMS experiment, corresponding to an integrated luminosity of 19.7 fb⁻¹. Events are selected having one electron or muon and at least four jets. The T-odd observables are measured using four-momentum vectors associated with (t\overline{t}) production and decay. The measured asymmetries exhibit no evidence for CP-violating effects, consistent with the expectation from the standard model.