Green basilisks, of course, are known as the Jesus Christ lizard because of their ability to run across the water, which is a fascinating thing for people and they often want to have them as pets. Not one of my highest recommendations, however. Because of their skittish nature they really don't do well in captivity unless you're a very experience keeper who knows enough to keep them in a huge, I mean huge, enclosure.
The larger, the better. An animal that gets up enough steam as far as his ability to run to hit the water and glide across it needs a lot of room and, unfortunately, a fish tank isn't the best place for him to be. He doesn't see the glass and basilisks often end up slamming into the side of the glass much like the Chinese water dragons do in Asia.
So, green basilisks are not my favorite. However, as far as a beautiful animal to keep in captivity, they get a beautiful blue hue to the side of them, they're straight insectivores, they're very, very attentive, they know what's going on, they're extremely fast and fun to watch but you've got to have a very, very big tank and that's all I can stress.
If you're going to keep an animal like this that's going to go at a moment's notice, you better make sure he doesn't hurt himself by ramming into the glass. So, a green basilisk is an option, certainly, for the advanced keeper if you can afford the space and the expense of having a very large tank, 125 gallons or more. You can make a basilisk a really interesting vivarium subject.