The benefits of Generative Artificial Intelligence (GenAI) in enhancing second language (L2) learning are well established. However, these advantages can only be realised if learners are willing to adopt the technology. This study, grounded in the Theory of Planned Behaviour (TPB), investigated the factors influencing the behavioural intention to use GenAI among 337 Chinese college L2 learners using five validated scales. A Structural Equation Modelling (SEM) approach with Amos 24 yielded several key findings. Notably, demographic factors encompassing gender and age did not significantly affect the TPB components. Subjective norm and attitude were found to have a positive and significant impact on behavioural intention, while perceived behavioural control did not demonstrate a significant effect. Furthermore, GenAI literacy emerged as a significant predictor of behavioural intention, both directly and indirectly through its influence on attitude. Collectively, these variables accounted for 51.6% of the variance in behavioural intention. The study also discusses the theoretical and pedagogical implications and offers suggestions for future research.