Chronic pain is a multi-dimensional experience, and pain intensity plays an important part, impacting the patients emotional balance, psychology, and behaviour. Standard self-reporting tools, such as the Visual Analogue Scale for pain, fail to capture this burden. Moreover, this type of tools is susceptible to a degree of subjectivity, dependent on the patients clear understanding of how to use it, social biases, and their ability to translate a complex experience to a scale. To overcome these and other self-reporting challenges, pain intensity estimation has been previously studied based on facial expressions, electroencephalograms, brain imaging, and autonomic features. However, to the best of our knowledge, it has never been attempted to base this estimation on the patient narratives of the personal experience of chronic pain, which is what we propose in this work. Indeed, in the clinical assessment and management of chronic pain, verbal communication is essential to convey information to physicians that would otherwise not be easily accessible through standard reporting tools, since language, sociocultural, and psychosocial variables are intertwined. We show that language features from patient narratives indeed convey information relevant for pain intensity estimation, and that our computational models can take advantage of that. Specifically, our results show that patients with mild pain focus more on the use of verbs, whilst moderate and severe pain patients focus on adverbs, and nouns and adjectives, respectively, and that these differences allow for the distinction between these three pain classes.