My wife has a Volkswagen Passat and we just moved into a place with a Chamberlain garage door opener that uses a rolling code. The normal VW instructions don't help you figure out how to program these types of garage door openers. I found some instructions on VW vortex which describe how to do this. I'm going to paraphrase the instructions here so people searching for this kind of thing can easily find it.
Park your VW in the garage and turn on the ignition (don't start it -- just turn it to "on" without starting). I find this easier than trying to run outside and inside.
One side of your Chamberlain garage door opener will have the radio underneath the plastic light bulb cover. It's the side where the wall remote wires come in (if there are wires). Pull down the light bulb cover and press and hold the "learn" button until it goes out. This resets the codes and none of your remotes will work anymore.
This part is exactly like the VW manual and is how the car grabs the frequency of the remote: go to your VW and press and hold the HomeLink key you want to program. When it starts blinking slowly, also press the button on your garage door remote and hold it down until the light blinks fast. Make sure to hold the remote up near the HomeLink panel. After it blinks fast, let go of both buttons.
Go press the "learn" button again on the garage door opener and it will light up solid (you don't need to hold it).
Now go back to your car and press the button you programmed before. Hold it until the garage door opener's lights blink, and you hear a click. Mission accomplished! If you press the button again, it will open the garage door.
As mentioned, your remote will no longer work. Go back to your garage door opener and press the "learn" button briefly, until it goes solid. Press the button on your remote and the garage door opener lights blink again. Your remote and your VW should both work.