The objective of this work was to implement a 3-D Lagrangian stochastic (also called random walk or Monte Carlo) diffusion method in the framework of the operational ADPIC (Atmospheric Diffusion Particle-In-Cell) code. The Random Displacement Method, RDM, presented here and implemented in the ADPIC code, calculates atmospheric dispersion in a purely Lagrangian, grid-independent manner. Some of the benefits of this approach compared to the previously-used ``particle-in-cell, gradient diffusion`` method are (a) a sub-grid diffusion approximation is no longer needed, (b) numerical accuracy of the diffusion calculation is improved because particle displacement does not depend on the resolution of the Eulerian grid used to calculate species concentration, and (c) adaptation to other grid structures for the input wind field does not affect the diffusion calculation. In addition, the RDM incorporates a unique and accurate treatment of particle interaction with the surface.