Wrap the bicycle chain into a compact lump, and heave it at the animal in much the same way as you would throw a ball or a smaller animal. This type of attack is largely ineffective, but may prove useful in specific circumstances. If you find yourself needing to attack a slow moving animal while in a seated position for example. In a lawn chair, attacking an insolent sloth in the sloth enclosure at the zoo is what I'm imagining, but please don't let that limit your own creativity.
Attacking an animal with a bicycle chain takes an enormous amount of mental discipline. A bicycle chain is itself a kind of untamed beast, and if you hope to master its sinuous wiles, you must learn to master your own chemical imbalances first.
There are three main emotions you may find yourself in when attacking animals with a bicycle chain:
Emotion #1: Fear
Fear can come from a lot of places. It might be exam-preparation stress, or the terror of facing a charging animal, or even the dread about what society will think when they find out what you're about to do to this duck. How you handle this fear is important - the adrenaline fear provides can cause your bicycle chain employing muscles to flex powerfully. Scientists call this Bicycle Chain Beast Mode or at least they would if they had any sense of showmanship.
Emotion #2: Ire
You've got good reason to be angry with the animals. You know who never has to pay any taxes? Animals. You know who shits wherever they like? Animals. You know who slept with your mother last night? etc... Animals can do whatever they want, wherever they want, and you're sitting there like a chump, pooing where you're told.
I've had enough with all your god damned rules toilet.