Take out the start key from the ignition or disconnect the spark plug to prevent the snowblower from accidentally starting while you're troubleshooting the loose choke lever.
Remove the screws from the shroud covering the carburetor; the type and number of screws varies by model. Lift the shroud off of the carburetor and set it aside. Reserve the removed screws for reassembly.
Examine the choke assembly. Check to ensure that the linkage pin is connected to both the choke lever and carburetor. Reinsert the linkage pin if you find that it's wiggled free of either component.
Inspect the screw on the choke lever mounting bracket. Tighten the screw if it appears loose.
Replace the carburetor shroud. Reinsert and tighten the removed screws. Return the start key to the ignition or reconnect the spark plug.