We present tight-binding calculations in the random-phase approximation of the optical response of Silicon nanocrystals (Si NCs) ideally doped with large concentrations of phosphorus (P) atoms. A collective response of P-induced electrons is demonstrated, leading to localized surface plasmon resonance (LSPR) when a Si NC contains more than ≈10 P atoms. The LSPR energy varies not only with doping concentration but also with NC size due to size-dependent screening by valence electrons. The simple Drude-like behavior is recovered for NC size above 4 nm. Si NCs containing a large number of deep defects in place of hydrogenic impurities do not give rise to LSPR.