With few exceptions, atomistic simulation work on polymers has been limited to linear chain systems. The main reason for this is the inability of existing Monte Carlo (MC) methods to equilibrate the short- and long-length scale characteristics of nonlinear polymers without destroying their complex molecular architecture. We report here the first MC simulation of a well-defined model long-chain branched polymer, the H-shaped polyethylene melt, in full atomistic detail. The simulation has been executed with an advanced set of chain connectivity-altering moves based on the end-bridging [Pant and Theodorou, Macromolecules 28, 7224 (1995); Mavrantzas , Macromolecules 32, 5072 (1999)] and double-bridging [Karayiannis , Phys. Rev. Lett. 88, 105503 (2002); Karayiannis , J. Chem. Phys. 117, 5465 (2002)] algorithms. The new scheme provides excellent system equilibration at all length scales. The new method opens up the way toward the simulation of other nonlinear polymer systems where chain branching is precisely known (such as stars and combs) and the study of their unique thermodynamic and rheological properties from first principles. (C) 2003 American Institute of Physics.