At what age should you let your child chew gum? I guess it depends on the child. When children begin eating solid food they are taught to chew and swallow, but gum doesn't work that way. I don't feel comfortable giving our children gum until they understand the concept of chewing without swallowing.
Our five year old has asked us for gum many times, but I'm always worried that she will swallow and choke on it. She's almost six years old, so one day she tried a piece and she liked it. She told me that she didn't swallow it and that she put it in the garbage. I was relieved, but I'm not in a rush to go out and buy her gum. Our four year old tried gum once and she didn't like it. I think she's still too young to understand how gum works.
Gum can be a choking hazard, so don't give your children gum until they're old enough. Be patient and when they're ready you will know.