It's not the LANGUAGE, it's the INTEREST (Score 1)

Here's the first question. What does the child want? I mean what is sparking his/her interest in wanting to learn to program. That's where I'd start.

I learned on basic and yes, it's a great language, but as others have said, don't under estimate your child. They learn a lot quicker than we do. If basic won't fit what sparks their interest then go with what does.

If the child would like to have a state of the art website with tons of programmed things, then teaching them html and javascript, perl, and php would be a great choice. If they want to write a game perhaps c/c++ would be the best language. Unfortunatly for a kid to write something that keeps up with the times isn't as easy to do starting out as it was say 10-15 years ago.

Taking that into account you might want to help guide them into choosing an achievable project while still doing something that interests them. This would keep them from being upset if it doesn't turn out looking like the coolest game currently off the shelf and ultimately keeping them from programming in the future.

Just my two cents.