Because the fusion of the hydrogen atoms creates intense heat, and if you fuse enough hydrogen you get oxygen.
Edit:
Question:
If there is no oxygen in space, how does the Sun "burn"?
Answer:
The Sun does not "burn", like we think of logs in a fire or paper burning. The Sun glows because it is a very big ball of gas, and a process called nuclear fusion is taking place in its core. Nuclear fusion occurs when one proton smashes into another proton so hard that they stick together...and release some energy as well. This energy then heats up the other materials (other protons and electrons and such) nearby. This heating eventually grows out from the center (or core) of the star to the outside, finally leaving the surface and radiating out into space to be the heat and light we know stars emit.
People, including scientists, sometimes say that the Sun "burns hydrogen" to make it glow. But that is just a figure of speech. Hydrogen really doesn't burn, it fuses, into helium. So no oxygen is required!
