Neural dialogue models, despite their successes, still suffer from lack of relevance, diversity, and in many cases coherence in their generated responses. These issues can attributed to reasons including (1) short-range model architectures that capture limited temporal dependencies, (2) limitations of the maximum likelihood training objective, (3) the concave entropy profile of dialogue datasets resulting in short and generic responses, and (4) the out-of-vocabulary problem leading to generation of a large number of <UNK> tokens. On the other hand, transformer-based models such as GPT-2 have demonstrated an excellent ability to capture long-range structures in language modeling tasks. In this paper, we present DLGNet, a transformer-based model for dialogue modeling. We specifically examine the use of DLGNet for multi-turn dialogue response generation. In our experiments, we evaluate DLGNet on the open-domain Movie Triples dataset and the closed-domain Ubuntu Dialogue dataset. DLGNet models, although trained with only the maximum likelihood objective, achieve significant improvements over state-of-the-art multi-turn dialogue models. They also produce best performance to date on the two datasets based on several metrics, including BLEU, ROUGE, and distinct n-gram. Our analysis shows that the performance improvement is mostly due to the combination of (1) the long-range transformer architecture with (2) the injection of random informative paddings. Other contributing factors include the joint modeling of dialogue context and response, and the 100% tokenization coverage from the byte pair encoding (BPE).