Chain shot can be tricky to use, but can give you a decisive edge if you know exactly how to use it.
The first rule of chain shot in this game (that I cannot emphasize enough): Do NOT use chain shot against MASTS. Don't think of it as an anti-mast weapon because chain shot is not designed to take out masts. Chain shot is designs to take out SAILS. This means you should only use chain shot IF AND ONLY IF an enemy has their sails unfurled.
Shooting while their sails are furled is wasted as it takes a very lucky shot to hit a mast and an incredibly lucky shot to cut down a mast. In that case you should use round shot to maximize your average damage per shot (i.e., to waste as few shots as possible).
Typically if you do enough damage to the sails and associated rigging, the masts will come down on their own. Don't think of it like the movie Master And Commander where the goal is to shoot the mast; instead the goal is to hit the sails and put as many holes in them as possible.
As mentioned in previous posts, the best way to use chain shot is when you are perpendicular to an enemy warship (and their sails are unfurled) because that presents the largest sail surface-area to your gunners
Chain shot will damage sails, which will slow down a ship. More holes = more places for the wind to slip through = lower maximum speed. Even a sloop or a brig can be brought almost to a complete stop by taking out its sails and masts, robbing it of its only advantage.
Typically chain shot is not useful in the opening of the battle (unless outnumbered and leeward -- see below). Generally I find it more effective to use round shot to damage enemy hulls and -- perhaps more importantly -- destroy their cannons. Typically I'll use chain shot in the later stages when I'm mopping up. I'll use chain shot against isolated, low morale (or routing) ships to prevent them from escaping. It's always better to capture than to sink an enemy, so it's worth using chain shot to prevent a potential prize from slipping away.
Another time to use chain shot is when you're outnumbered and leeward.* I've devised a strategy for fighting a superior opponent by using chain shot, although admittedly with mixed results. Since the opposing force will be windward and charging at me, their sails will be out virtually the whole time. My goal is to slowly retreat to the leeward while making 180 degree turns snaking back and forth (this does two things: 1) it allow my gunners on the other side of the ship to fire at the enemy, which can be faster than simply waiting for the first side to reload; and 2) it spreads out the damage I take from the enemy and lets my ship stay afloat longer). As I retreat, I use chain shot on ONE enemy ship; when its sails are significantly damaged, I focus on a new enemy.
The goal here is to slowly isolate and spread out the enemy fleet. The first ship can't keep up with the rest of its fleet and falls behind. So does the second ship. Then the third. Eventually their fleet will be spread out and I can then engage individual ships rather than their superior fleet. Basically, divide and conquer. It works on paper but it's difficult in practice.
* "Leeward" essentially means "down wind" -- for example: if the wind is blowing from the north to the south, and there are two ships--one is to the north and the other to the south--then the southern ship is leeward while the northern ship is windward.