If there is no oxygen in space, how does the Sun burn?

Molecular oxygen does occur in space, but it is very scarce. However, even if there were a lot of it, it is not the reason for the “burning” of the Sun.
Earth is the only place in our solar system where there is fire. It is known that flames require free atmospheric oxygen, and the Earth has about 21% of it. The Sun, on the other hand, is composed mostly of hydrogen (91 %) and helium (8.9 %). The remainder, including oxygen, makes up a very small fraction of the mass.