This paper describes the Omphalos Context-Free Grammar Learning Competition held as part of the International Colloquium on Grammatical Inference 2004. The competition was created in an effort to promote the development of new and better grammatical inference algorithms for context-free languages, to provide a forum for the comparison of different grammatical inference algorithms and to gain insight into the current state-of-the-art of context-free grammatical inference algorithms. This paper discusses design issues and decisions made when creating the competition. It also includes a new measure of the complexity of inferring context-free grammars, used to rank the competition problems.