Parallelization of standard multigroup methods used to solve the linear (Boltzmann) tranaport equation in the discrete ordinates (Sn) representation and coupled chaotic iteration schemes are the focus of this analyais. On the Denelcor HEP, we extend two serial iteration schemea, categorize speedup, and contrast ordered and chaotic methods. Ordered and chaotic iteration atrategies, with arid without acceleration, support relatively unreatricted paralleliam and appear to be robust parallel techniques. Parallel modifications and recoding efforts to seriol iteration algorithms are straightforward, actual speedup and efficiency are high, and payoff appears substantial, largely due to the coarse computational granularity of the multigroup technique. Chaotic schemes also converge faster than ordered strategies.