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Over the last few years, the size range of objects appropriate for optical trapping at room temperature has been significantly expanded into the nanoscale, and currently reaches dimensions of single viruses and proteins. This has become possible due to the use of photonic-crystal and plasmonic resonators providing high localization of electromagnetic fields so that particles of smaller dimensions can be trapped. Having negligible ohmic losses, photonic-crystal resonators have a significant advantage over plasmonic ones, a property especially important for biological applications. On the other hand, plasmonic resonators are much more compact and can be integrated onto tips of tapered fibers, providing three-dimensional manipulation of nanoobjects. A new player in the field, all-dielectric Mie-resonant nanostructures, combine the above advantages, being at once low-loss and compact. This makes a great prospect for using them as a perfect tool for optical trapping. We report on an experimental study of optical trapping of a single dielectric nanoparticle in the near field of a silicon nanodisk dimer. The disks were made using electron beam lithography with subsequent reactive ion etching and characterized by scanning electron microscopy and dark-field scattering spectroscopy. In the trapping experiments, optical tweezers based on a tightly focused infrared laser beam were used. Statistics of trapping of 100-nm polystyrene beads suspended in water was studied in two cases: with the beam focused in water, as in conventional optical tweezers, and near a silicon dimer providing enhancement of the electric field in the gap between the two disks as predicted by numerical calculations. Measurements show the enhancement of the trapping stability in the near field of a silicon dimer, paving a way to low loss laser trapping at the nanoscale.