OBS - Steam - One monitor chat in game

First, make sure that in the OBS Window capture you do NOT have it set to capture third party overlays. 

*Note: This won't work nicely with screen capture, but you shouldn't use that anyway because it's worse performance.

Step 1: Open a game up through Steam.

Step 2: Press Shift+Tab to open the Steam Overlay

Step 3: Click at the bottom to show website.

Step 4: Enter your chat URL with for the pop-up: https://www.twitch.tv/popout/<your channel>/chat?popout=

Step 5: Arrange the window size to be what you want.
 

Step 6: Click to set the pin, and set opacity.
 

Now press Shift+Tab to go back to the game, and the chat will be there while Stream cannot see it.