Try to figure out what is causing you to chew ice cubes in the first place. It could be a sign of stress or a more serious medical condition, such as iron-deficiency anemia. Perhaps a multi-vitamin with iron is all you need to help you stop your habit.
More than likely, though, you are just chewing on ice because you are bored and still sitting at the table after you have finished your food. There are also some people who just like chewing ice.
4 Reasons Why Chewing Ice Cubes Hurts Your Teeth
1 - Chewing ice puts an enormous amount of pressure on your teeth. While the dentin in your teeth is relatively flexible, the enamel is very hard and doesn't flex much. Chewing ice can wear down the enamel and even chip or fracture pieces of the enamel off of your teeth.
2 - Chewing ice causes a repetitive hot/cold cycle in your mouth. This can cause microcracks in your enamel over time. Also, tooth enamel expands at a different rate than fillings. If you have a white filling, it will expand and contract much faster than the tooth when exposed to hot and cold temperatures. This could lead to a breakdown of the seal at the tooth/filling interface and may shorten the life of your filling.
3 - If you have braces, the ice could damage them. It might break off a bracket or move a wire, making it ineffective at doing its job of bringing your teeth into proper alignment.
4 - It can damage your gums. Ice chunks are hard and can be pretty sharp. Although I don't know of any studies to back this up, it would seem that if you are constantly chewing ice and pressing down on the gums, you could cause injury to your gums and perhaps even cause gum recession. For example, tongue rings press on the surface of your teeth closest to your tongue and have been shown to cause gum recession in these areas.