The formation mechanism of the ice giant planets is uncertain. A new hypothesis envisions rapid formation of several gaseous protoplanets in a marginally gravitationally unstable protoplanetary disk, and coagulation and settling of dust grains within the protoplanets to form rock and ice cores, followed by the loss of the outer disk gas and the gaseous envelopes of the protoplanets through photoevaporation driven by nearby OB stars. We demonstrate here that the first part of this new scenario for ice giant planet formation is feasible in a disk with a gas density similar to that believed to be necessary to form the giant planets. A three-dimensional gravitational hydrodynamics code, including a full treatment of thermodynamics and radiative transfer in the diffusion approximation, is used to show that a disk is likely to form two or more gravitationally bound clumps, with masses on the order of 2 Jupiter masses, between 20 and 30 AU from a solar-mass star. Such protoplanets could be massive enough to explain the production of Uranus and Neptune following photoevaporation of most of their gaseous envelopes. This scenario implies that planetary systems similar to our own could form even in seemingly hostile regions of high-mass star formation.