Twitter is one of the most popular online micro-blogging and social networking platforms. This platform allows individuals to freely express opinions and interact with others regardless of geographic barriers. However, with the good that online platforms offer, also comes the bad. Twitter and other social networking platforms have created new spaces for incivility. With the growing interest on the consequences of uncivil behavior online, understanding how a toxic comment impacts online interactions is imperative. We analyze a random sample of more than 85,300 Twitter conversations to examine differences between toxic and non-toxic conversations and the relationship between toxicity and user engagement. We find that toxic conversations, those with at least one toxic tweet, are longer but have fewer individual users contributing to the dialogue compared to the non-toxic conversations. However, within toxic conversations, toxicity is positively associated with more individual Twitter users participating in conversations. This suggests that overall, more visible conversations are more likely to include toxic replies. Additionally, we examine the sequencing of toxic tweets and its impact on conversations. Toxic tweets often occur as the main tweet or as the first reply, and lead to greater overall conversation toxicity. We also find a relationship between the toxicity of the first reply to a toxic tweet and the toxicity of the conversation, such that whether the first reply is toxic or non-toxic sets the stage for the overall toxicity of the conversation, following the idea that hate can beget hate.