Contactless manipulation of micron-scale objects in a microfluidic environment is a key ingredient for a range of applications in the biosciences, including sorting, guiding, and analysis of cells and bacteria. Optical forces are powerful for this purpose but, typically, require bulky focusing elements to achieve the appropriate optical field gradients. To this end, realizing the focusing optics in a planar format would be very attractive and conducive to the integration of such microscale devices, either individually or as arrays. Here we report on, to the best of our knowledge, the first experimental demonstration of optical trapping using planar silicon metalenses illuminated with a collimated laser beam. The structures consist of high-contrast gratings with a locally varying period and duty cycle. They are designed to mimic parabolic reflectors with a numerical aperture of 0.56 at a vacuum wavelength of 1064 nm. We achieve both two- and three-dimensional trapping in water, with the latter realized by omitting the central Fresnel zones. This Letter highlights the versatility of such lithographically defined metastructures for exerting optical forces without the need for traditional optical elements.