We introduce optical solenoid beams, diffractionless solutions of the Helmholtz equation whose diffraction-limited in-plane intensity peak spirals around the optical axis, and whose wavefronts carry an independent helical pitch. Unlike other collimated beams of light, appropriately designed solenoid beams have the noteworthy property of being able to exert forces on illuminated objects that are directed opposite to the direction of the light's propagation. We demonstrate this through video microscopy observations of a colloidal sphere moving upstream along a holographically projected optical solenoid beam.