Chemical and physical properties of binary metallic nanoparticles (nanoalloys) are to a great extent defined by their chemical ordering, i.e. the pattern in which atoms of the two elements are located in a given crystal lattice. The reliable determination of the lowest-energy chemical ordering is a challenge that impedes in-depth studies of several nm large bimetallic particles. We propose a method to efficiently optimize the chemical ordering based solely on results of electronic structure (density functional) calculations. We show that the accuracy of this method is practically the same as the accuracy of the underlying quantum mechanical approach. This method, due to its simplicity, immediately reveals why one or another chemical ordering is preferred and unravels the nature of the binding within the nanoparticles. For instance, our results provide very intuitive understanding of why gold and silver segregate on low-coordinated sites in Pd70Au70 and Pd70Ag70 particles, while Pd70Cu70 exhibits matryoshka-like structure and Pd70Zn70 features Zn and Pd atoms arranged in layers. To illustrate the power of the new method we optimized the chemical ordering in much larger Pd732Au731, Pd732Ag731, Pd732Cu731, and Pd732Zn731 nanocrystals, whose size ~4.4 nm is common for catalytic applications.