Single photon sources with high brightness and subnanosecond lifetimes are key components for quantum technologies. Optical nanoantennas can enhance the emission properties of single quantum emitters, but this approach requires accurate nanoscale positioning of the source at the plasmonic hotspot. Here, we use plasmonic nanoantennas to simultaneously trap single colloidal quantum dots and enhance their photoluminescence. The nano-optical trapping automatically locates the quantum emitter at the nanoantenna hotspot without further processing. Our dedicated nanoantenna design achieves a high trap stiffness of 0.6 (fN/nm)/mW for quantum dot trapping, together with a relatively low trapping power of 2 mW/μm2. The emission from the nanoantenna-trapped single quantum dot shows 7× increased brightness, 50× reduced blinking, 2× shortened lifetime, and a clear antibunching below 0.5 demonstrating true single photon emission. Combining nano-optical tweezers with plasmonic enhancement is a promising route for quantum technologies and spectroscopy of single nano-objects.