Tree-based classifiers are important in pattern recognition and have been well studied.  Although the problem of finding an optimal decision tree has received attention, it is a hard optimization problem.  Here we propose utilizing a genetic algorithm to improve on the finding of compact, near-optimal decision trees.  We present a method to encode and decode a decision tree to and from a chromosome where genetic operators such as mutation and crossover can be applied.  Theoretical properties of decision trees, encoded chromosomes, and fitness functions are presented.