We optically trap freestanding single metallic chiral nanoparticles using a standing-wave optical tweezer. We also incorporate within the trap a polarimetric setup that allows us to perform in situ chiral recognition of single enantiomers. This is done by measuring the S_{3} component of the Stokes vector of a light beam scattered off the trapped nanoparticle in the forward direction. This unique combination of optical trapping and chiral recognition, all implemented within a single setup, opens new perspectives towards the control, recognition, and manipulation of chiral objects at nanometer scales.