We simulate the formation of planetary systems around α Centauri B. The N-body accretionary evolution of a Σ ∝ r−1 disk populated with 400-900 lunar-mass protoplanets is followed for 200 Myr. All simulations lead to the formation of multiple-planet systems with at least one planet in the 1-2 M⊕ mass range at 0.5-1.5 AU. We examine the detectability of our simulated planetary systems by generating synthetic radial velocity observations including noise based on the radial velocity residuals to the recently published three planet fit to the nearby K0 V star HD 69830. Using these synthetic observations, we find that we can reliably detect a 1.8 M⊕ planet in the habitable zone of α Centauri B after only 3 years of high cadence observations. We also find that the planet is detectable even if the radial velocity precision is 3 m s−1, as long as the noise spectrum is white. Our results show that the greatest uncertainty in our ability to detect rocky planets in the α Centauri system is the unknown magnitude of ultralow frequency stellar noise.