Research in Psychology has shown that stories people tell about themselves, and how they recall their experiences, reveal a lot about their individual characteristics and mental well-being. The Narrative Coherence Coding Scheme (NaCCS) is a set of guidelines established in psychology research for annotating the "coherence"of a narrative along three dimensions: context, chronology and theme. A significant correlation was found between a narrative's coherence score and independently collected mental health markers of the narrator. Currently, all coherence annotations are done manually; a time consuming task which drains vital resources. In this paper, we propose an Artificial Intelligence based approach involving Natural Language Processing (NLP) to predict a narrative's coherence score (4-class classification problem). We explore a number of techniques, ranging from traditional machine learning models such as Support Vector Machines (SVM) to pre-trained language models such as BERT (Bidirectional Encoder Representations from Transformers). BERT produced the best results for all dimensions in terms of accuracy: 53.7% (context), 71.8% (chronology), and 69.6% (theme). The location of information in the narratives (beginning, end, throughout) was helpful in improving predictions.