A new type of stable alternating-beam light trap is proposed for confinement of neutral atoms and macroscopic dielectric particles. This trap, based only on the scattering force of radiation pressure, overcomes the limitations of the optical Earnshaw theorem. Trapping of ~10(7) sodium atoms in large volumes (100 cm(3)) seems possible with well depths >1 K and with optical cooling close to the Purcell limit of ~10(-4) K. Trapping at points of zero light intensity is considered.