When you get a brand-new bicycle chain, hung it up, and carefully started adding weight to the end, your answer would probably be in the high hundreds, if not thousands of pounds. But the problem is, that’s not how bicycle chains are used.
In real life usage, bicycle chains are often skewed (each gear, front and back, skews the chain line to one side or another), worn, and have extremely irregular forces being applied to them.
A typical bicycle chain has the breaking strength on the order of 1000 kgf. It must withstand 200 lb of tension for hours on end without permanent deformation, merely because that’s the amount of tension it would experience during pedaling out of the saddle. A chain rated to 1300 kgf should be able to lift a weight of 1300kg (2860 pounds). This might sound a lot but when you get a fairly large bloke jumping on cranks fitted with tiny sprockets forces can get quite high. For example, a 250 lb bloke standing on a 170mm (6.69") cranks fitted with a 12 tooth sprocket (1.91"radius) will cause about 875 pounds force in the chain at the sprocket. (Torque = force x distance). If he jumps, it will be much higher. This is when chains break.
bike chain, weight
A cyclist riding with a cadence of 90 rpm and putting out about a quarter horsepower will only be applying about 28 lbs force to the pedals that is far, far less than that could break the chain. As a matter of fact, there’s basically no chance of you pulling it apart with your bare hands as long as you’re pulling along the length of the chain, even if you’re an international-level weightlifter. The bike chain should be plenty strong enough to handle a 2 hp chainsaw engine.
However, it is a different story if you are on a stretched chain or in combination with worn freewheel cogs when you will easily make one slip forward one or more cogs per push which severely inhibits forward motion. The chains typically fail by the link plate on one side working its way off of the pin, and then the other side twisting under the uneven force, and either ripping the pin out of the remaining plate or having the pin slip out of the roller. Either way, the chain is then separated.
On a new sprocket tooth, the surface that the roller presses against is perpendicular to the pull of the chain. The worn chain that is "stretched" no longer matches the original pitch of the sprocket. The worn teeth have become ramps, causing the chain to ride up under load. In this way, even the most expensive chains are not the strongest if the connecting plate mismatches appear.
bike chain, weight
If you have broken a chain once during sprints by pushing with much effort down on one pedal and simultaneously upon the other pedal, the real reason should be the chain is so worn that the link plate slips from the pin or there is a crack which starts from the link pin hole and it get worse with use until the chain broke, which is almost impossible for the strong stainless chain material.
On the basis of the analysis above, what counts is to maintain the chain carefully to expand its lifespan and ensure the match of cogs and the chain. Chains will fail eventually with wear, rather than least possible crack, any sort of things that get caught in it, (including body parts) and you are still in danger of a sprocket or chain coming off and embedding itself. So it would be recommended to use a chain guard and conduct regular cleaning.
Chains lengthen over time as they wear down. A worn chain will also wear out the cogs in the front and rear cassette—starting with the most used gears. If you put a new chain on, the worn gears will wear it down even faster than normal. So you need to replace the entire drive chain or use this opportunity to get a new bike. You can buy a bike chain measuring tool from a bike shop or online to monitor the length of the chain, it will indicate when the chain is getting close to needing to be replaced.
On an old bike, that strongly suggests that your cogs are worn out and need to be replaced. Chains wear faster than cogs but they tend to wear together, so an old chain and old cogs might still match up alright, but then you put a brand new chain on the worn cogs and it jumps all over the place. In fact, if you still have it and can connect it, try again with the old chain.
bike chain, weight
In a nutshell, a bike chain could withstand much more forces when you are cycling than you could exert unless slips happen. Generally speaking, a well-maintained chain can be used for 5 to 10 years.