We have assembled three-dimensional heterotypic networks of living cells in hydrogel without loss of viability using arrays of time-multiplexed, holographic optical traps. The hierarchical control of the cell positions is achieved with, to our knowledge, unprecedented submicron precision, resulting in arrays with an intercell separation <400 nm. In particular, we have assembled networks of Swiss 3T3 fibroblasts surrounded by a ring of bacteria. We have also demonstrated the ability to manipulate hundreds of Pseudomonas aeruginosa simultaneously into two- and three-dimensional arrays with a time-averaged power <2 mW per trap. This is the first time to our knowledge that living cell arrays of such complexity have been synthesized, and it represents a milestone in synthetic biology and tissue engineering.