Tight Θ(n^2) bounds are known for the total step complexity of randomized algorithms for n-process consensus from registers [1]. However, there is a large gap between the best known space lower bound of Ω(sqrt(n)) registers and the Θ(n) space complexity of the best existing algorithms. We prove matching upper and lower bounds of n for the space complexity of nondeterministic solo-terminating consensus in a restricted computational model.