What is the biggest star in the Universe?

My six-year old daughter is a question asking machine. We were driving home from school a couple of days ago, and she was grilling me about the nature of the Universe. One of her zingers was this, "What's the Biggest Star in the Universe"? I had an easy answer, the Universe is a big place, and there's no way we can possibly know what the biggest star is. That didn't go over so well. So she refined the question. What's the biggest star that we know of?

Of course, I was stuck in the car, and without access to the Internet. But now I'm back at home, doing some research, and I thought I'd share the answer with the rest of you too.

Before we jump straight to the answer, let's take a look at our own Sun for a sense of scale. Our familiar star is a mighty 1.4 million km across (870,000 miles). That's such a huge number that it's hard to get a sense of scale. The Sun accounts for 99.9% of all the matter in our Solar System. In fact, you could fit one million planet Earths inside the Sun.