In Daredevil Season 2, Stick tells Matt the story of the Chaste, with Matt replying
Now, in this fairy tale you're the Chaste, right?
Though Stick himself tells that this story started centuries ago
Sit down, Matty. It all began centuries ago. Nobody knows how many, but the shit we're dipping into is ancient.
Also from Iron Fist we know that whole The Hand story started in Kun'Lun and the elders of the Hand have lived several lifetimes due to being resurrected with "substance".
Therefore, one of two conclusions follow: either Stick is not the Chaste, or he has been desecrating Shou-Lao as well to live that long.
So which case is that?
Note per comments: about that kid being the Chaste, not just the organisation.
Some say it was just a kid. Hand comes into his village, kills everyone almost. Kid pulls the knife from the breast of his dead mother and goes to work. He cuts down some of the Hand's finest warriors. They're lying dead kid's standing. They give him a name. The Chaste.