Since its atmosphere is made of 90% hydrogen.
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https://www.quora.com/Can-hydrogen-burn-without-oxygen From the couple minutes of research and googling I just did to figure it out, it depends on what else is in Jupiter's atmosphere and how much is in it. For a flammable substance (hydrogen, in this instance), a proper amount of oxidizer needs to be present. The oxidizer can be oxygen, but it doesn't have to be; halogens can work just as well. But if there's isn't enough oxidizer, it won't last long enough to, say, combust the entire planet.