Hi Nina,
There can be a number of reasons why rabbits have leaky eyes but the most common one is from a blocked tear duct. this site has some useful hints on rabbit health problems. .http://www.rabbitnetwork.org/articles/eyes.shtml
and this is what it has to say about eye problems.
“Blocked tear ducts: Dental problems, inflammation, and other sources can clog your bunny’s tear (nasolacrimal) ducts. The ducts run from the inner corner of the eye to the nose and drain the liquid tear film that is constantly formed to protect the eye (this is why when you cry, your nose gets runny). Rabbits only have one duct opening in the eye, and thus are more susceptible to blocks. The tears, instead of draining out, then overflow and leave wet areas around the eye. The condition itself is not painful, but constant tears on the face will cause skin irritation. Without care, the fur becomes soggy and matted around the eye, and the underlying skin will become so irritated that eventually the fur just peels off- events should never get to this point. Until the duct opens, which may take several visits to the vet, gently wipe your bunny’s affected eye several times a day to remove the sticky salty tears (try cotton wipes and water), then dry carefully”
Also its importnat that you dnt make a self diagnosis and that you do get chestnut seen by a vet.