You can add a chat to your event site under Audience interactions. Enable Chat toggle to show chat on your event site.
You can have a chat functionality with 1) open chat or 2) moderated chat.
1) Open chat: If you disable the moderation option, you'll have an open chat. This means that all the comments sent by attendees are shown automatically to everyone on the event site.
2) Moderated chat: You can create a moderated chat, where you can control which messages are shown on the event site.
Enable this feature, if you want to have chat next to the Video and slides on their right side, not below. Usually this option is disabled and the chat is placed under the video and slides. If you're not using slides, this is not relevant for you.
Enable this feature to have messages next to each other as a chat wall (left image) instead of a linear chat stream (right image). This way you can ensure a compact event site.