Self-attentional models are a new paradigm for sequence modelling tasks which differ from common sequence modelling methods, such as recurrence-based and convolution-based sequence learning, in the way that their architecture is only based on the attention mechanism. Self-attentional models have been used in the creation of the state-of-the-art models in many NLP task such as neural machine translation, but their usage has not been explored for the task of training end-to-end task-oriented dialogue generation systems yet. In this study, we apply these models on the DSTC2 dataset for training task-oriented chatbots. Our finding shows that self-attentional models can be exploited to create end-to-end task-oriented chatbots which not only achieve higher evaluation scores compared to recurrence-based models, but also do so more efficiently.