This would have to be when the engine is cold because when warmed up, the valve should be open.

So assuming it is cold:

This tells me that when the choke valve is closed there is too much gas being pulled into the engine.

• Check the fast idle. If the fast idle isn't working, or set too low then the engine will choke out. The fast idle opens the throttle valve so that more air is used.
• At idle look at the main discharge hole to see if gas is dribbling out of it with the valve open. That would indicate gas is getting siphoned from the main discharge maybe due to the check ball not seating, or check weight above the check ball missing. Also test the check ball to make sure it is seating.
• Be sure the gas cap is vented. You can usually tell this by driving for awhile, then remove the gas cap. A non vented cap will cause a suction.