A method for reconstituting a connectivity matrix from a list of fragments is described. The Genetic Algorithm is used to obtain connectivity matrices that satisfy chemical correctness rules and match the given fragment list. A brief description of the genetic algorithm is made, and the encoding method and fitness evaluation function are described in detail. Performance of this system is described on eight molecules having from 8 to 25 backbone atoms. The software builds satisfying connectivity matrices for all of the examples, albeit with varying success rates and computation times. Simulated evolution, being a stochastic process, does not behave repeatably, and statistics over 500 runs are presented for each molecule. The software used is available freely to let readers replicate the results and test the method on the examples presented or on the fragment list of their choice.