Without a thorough exam, it would be difficult to say why this is happening. It sounds like you're saying just one eye is watery. As long as the liquid is clear, not bubbly, milky or greenish, I wouldn't worry about it much. It's very good to notice things like this. Good sign of a watchful chicken keeper. For this to go on for so long tells me that maybe this chicken was injured or hatched with a defect to the tear duct. As long as it's not infected you shouldn't need to do much about it.
If it were my chicken I would catch it and inspect the eye for any foreign particle or small object that may be stuck between the eye ball and eye lid. Flushing out the eye with a sterile eye wash might help dislodge anything, like a grain of sand, that could be irritating the eye and causing the excessive tear production.
The way chickens like to scratch in the dirt, it would be easy for one chicken to fling particles in the direction of another chicken. If this is a result of an injury, this chicken may have this extra watery eye for the rest of its life; or it could repair over time. I doubt this is causing the chicken any trouble as long as there is no sign of swelling or infection.
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