I hate to break it to you but chains don't stretch unless they're damn close to breaking.
Think: If the metal is under enough tension to cause it to stretch, when would it stop stretching?...well, it wouldn't, until it broke.
Chain "stretch" is wear between the rollers and the pins, and the pins and the links. A new chain is nice n' tight like your sweetest high school memories, but because very few chain manufacturers will take the time (and because you won't take the dough) to polish-fit each pin, and each link-hole, the pins and holes burnish in giving you the initial "stretch".
The sprockets (not "gears" in a chain-drive setup) don't wear much at all.
Think: Rollers. They're stationary when they're riding round the sprocket. The rolling is in between the roller and pin. This is why modern motorcycles use o-ring chains; to keep the lube in and dirt out of rollers and pins.
As the wear commences, the centerlines of the pins grow further apart, and this causes the chain to contact the leading or trailing edge of the sprocket tooth where it has minimal contact area so the loading is very high. When it's new, the chain rides in the valley of the tooth where there's tons of contact area and the load is spread out.
So the sprocket essentially gets hammered out of shape over time, not worn, because the rollers are no longer hitting where they're supposed to. The teeth actually grow in length as they're hammered to be thinner in profile. And your new chain doesn't get guided to the valley of the tooth on the worn sprockets...so your new chain gets "hammered" to match the old sprocket, in short (and expensive) order.
Not that it matters one bit, but I've replaced a billion motorcycle chains n' sprockets in my life (and a few timing chains, too), and the vernacular is mis-leading. Correct answer: During normal wear the chain does not stretch and the sprockets do not wear. The chain wears and the sprocket gets hammered.
An improperly heat-treated chain can stretch, but usually just a little before it's stretched in two.