The Neural Grammar Network is a novel machine learning system that is designed to accept formal language strings as input, and associate each with a real-valued output vector. This is accomplished by combining the syntactic structuring capability of the formal language parser and the general function approximation utility of the heterogeneous dynamic recursive artificial neural network. In this thesis, the NGN is demonstrated as a viable option for the example Quantitative Structure Activity Relationship problem space in computational chemistry. It is shown in this work, that the NGN is capable of achieving classification accuracy for one QSAR problem within 3% of the leading method, and outperforms all other compared methods in 6 out of 9 regression tasks on average. The NGN fills the niche in machine learning culture wherever syntactic learning of a formal language is too costly or not required for the goal of semantic inference.