Online communication channels, especially social web platforms, are rapidly replacing traditional ones. Online platforms allow users to overcome physical barriers, enabling worldwide participation. However, the power of online communication bears an important negative consequence --- we are exposed to too much information to process. Too many participants, for example, can turn online public spaces into noisy, overcrowded fora where no meaningful conversation can be held. Here we analyze a large dataset of public chat logs from Twitch, a popular video streaming platform, in order to examine how information overload affects online group communication. We measure structural and textual features of conversations such as user output, interaction, and information content per message across a wide range of information loads. Our analysis reveals the existence of a transition from a conversational state to a cacophony --- a state of overload with lower user participation, more copy-pasted messages, and less information per message. These results hold both on average and at the individual level for the majority of users. This study provides a quantitative basis for further studies of the social effects of information overload, and may guide the design of more resilient online communication systems.