I was looking for this today, and here's what I found:

Open Chat

• Ctrl + Shift + I
• Ctrl + Alt + B (Note: This option won't focus the textbox)

Close Chat

• Ctrl + Alt + B (Focus will return to the last place used in the editor)

Return Focus to Editor Without Closing Chat

• Ctrl + G and then select the line number
• Ctrl + Shift + E (Press E twice to return to the editor)