The parton-level top quark (t) forward-backward asymmetry and the anomalous chromoelectric (d^t) and chromomagnetic (μ^t) moments have been measured using LHC pp collisions at a center-of-mass energy of 13 TeV, collected in the CMS detector in a data sample corresponding to an integrated luminosity of 35.9 fb−1. The linearized variable A(1)FB is used to approximate the asymmetry. Candidate tt¯ events decaying to a muon or electron and jets in final states with low and high Lorentz boosts are selected and reconstructed using a fit of the kinematic distributions of the decay products to those expected for tt¯ final states. The values found for the parameters are A(1)FB=0.048+0.095−0.087(stat)+0.020−0.029(syst),μ^t=−0.024+0.013−0.009(stat)+0.016−0.011(syst), and a limit is placed on the magnitude of ∣∣d^t∣∣< 0.03 at 95% confidence level.