Large language models (LLMs), despite being trained primarily on a word prediction task, show remarkable language production and comprehension abilities. Whereas larger and more recent models have achieved partial success on various pragmatic tasks, most have only been evaluated on their ability to draw “mandated” pragmatic inferences (e.g., implicature, presupposition) in which the felicity of a sentence is at stake. In this study, we focus on conversational elicitures (Cohen & Kehler, 2021), a type of non-mandated pragmatic inference that, in the class of cases considered here, involves the potential inference of a causal relation between a proposition denoted by a matrix clause and one derived from a relative clause associated with a direct object (e.g., in sentences like “Melissa detests the children who are arrogant and rude”, the inference that the detesting is a result of the arrogance/rudeness). We investigate whether LLMs are able to draw such inferences and use them in downstream syntactic processing. Our results suggest that larger and more recent models do in fact exhibit these capabilities, at least to some degree.