If you are using a simple iframe to embed your chat box, you'll need to edit the HTML for your web page and set width to 100%. Height can also be set to 100%, but more commonly setting width to 100% is what you are after.
LibraryH3lp chat boxes are inherently responsive. However if you are using a chat snippet to include chat on your web page AND you've chosen an embedded chat box style, you'll need to take an extra step to ensure the chat box is responsive within its parent container since embedded chat boxes become part of the content of your web page.
For snippets with embedded chat box styles, go the the chat snippet management page of the admin dashboard. Locate your chat snippet and edit it, setting width to 100%. Height can also be set to 100%, but more commonly setting width to 100% is what you are after.