This paper proposes a novel approach to the induction of Combinatory Categorial Grammars (CCGs) by their potential affinity with the Genetic Algorithms (GAs). Specifically, CCGs utilize a rich yet compact notation for lexical categories, which combine with relatively few grammatical rules, presumed universal. Thus, the search for a CCG consists in large part in a search for the appropriate categories for the data-set’s lexical items. We present and evaluates a system utilizing a simple GA to successively search and improve on such assignments. The fitness of categorial-assignments is approximated by the coverage of the resulting grammar on the data-set itself, and candidate solutions are updated via the standard GA techniques of reproduction, crossover and mutation.