We have a few banana trees in our backyard and the dogs LOVE them. The browning leaves are their favorite chew thing. Cosmo loves to carry them around while Cocoa prefers to use the leaves in tug-o-war. Dewy loves to just chew and slurp on them and Dude hides them under dog beds for a saved snack for later.
As a word of advice, a bit or two of banana FRUIT is actually good for your chichi – the extra vitamins are a plus. So for all of you with banana trees in your yard – the leaves AND the fruit make a wonderful addition for your Chihuahua 🙂