Alpha Centauri B belongs to a triple star system comprised of a central A/B binary and a third companion, Proxima Centauri. The system, our closest stellar neighbor, is of great interest for planet hunters because it may harbor Earth-mass planets possibly in the habitable zone of the stars of the A/B binary. To assess whether terrestrial planets can indeed form around these stars, we run a series of N-body accretionary simulations of a 1/r disk populated with 400-900 lunar-mass oligarchs 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_Earth 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. Using these synthetic observations, we find that we can reliably detect a 1.8 M_Earth planet in the habitable zone of Alpha Centauri B after only three years of high cadence observations. The observations will be carried out at the CTIO site in northern Chile on a 1.5-m underutilized telescope. We expect to report the detection (or non-detection) of Earth-like planets around Alpha Centauri B in 3 to 5 years.