We report selective trapping of chiral nanoparticles via vector Lissajous beams. Local optical chirality densities appear in these beams by properly choosing the values of two parameters (p,q) that determine the polarization vectors of light. For a particular set of parameter (p,q) = (2,1) which is found preferable for the selective trapping, the resulting vector beam has two dominant intensity spots with opposite chirality. In the transverse plane, one spot traps a chiral particle while the other one repels the same particle under appropriate conditions, which can be reversed for a particle of opposite chirality. Various chiral parameters and radii of a particle are considered for analyzing this selective trapping effect. The longitudinal forces that are found non-conservative are also discussed. The achieved functionality of identifying and separating different chiral particles may find applications in enantiomer separation and drug delivery in pharmaceutics.