We report on the use of Neem (Azadirachta indica) leaf broth in the extracellular synthesis of pure metallic silver and gold nanoparticles and bimetallic Au/Ag nanoparticles. On treatment of aqueous solutions of silver nitrate and chloroauric acid with Neem leaf extract, the rapid formation of stable silver and gold nanoparticles at high concentrations is observed to occur. The silver and gold nanoparticles are polydisperse, with a large percentage of gold particles exhibiting an interesting flat, platelike morphology. Competitive reduction of Au3+ and Ag+ ions present simultaneously in solution during exposure to Neem leaf extract leads to the synthesis of bimetallic Au core-Ag shell nanoparticles in solution. Transmission electron microscopy revealed that the silver nanoparticles are adsorbed onto the gold nanoparticles, forming a core-shell structure. The rates of reduction of the metal ions by Neem leaf extract are much faster than those observed by us in our earlier studies using microorganisms such as fungi, highlighting the possibility that nanoparticle biological synthesis methodologies will achieve rates of synthesis comparable to those of chemical methods.