Refer to the Multiplayer chat example included in Construct 2.
Go to File -> New -> Multiplayer chat example
In the "Chat event" event sheet, under the group "Chat log", you can see that it uses a Textbox, set to read-only, where you set the text in a function to "Self.Text & newline & Function.Param(0)" and scroll to the bottom.
Each time, you want to add something to the chat, call the function with the Parameter containing the text you want to add.