Which chemical element makes up most of the Sun?

Hydrogen - about 73 per cent by mass, with helium making up most of the rest and everything else amounting to under two per cent. That is roughly the composition of the universe, because the Sun is made of unprocessed material from the cloud it condensed out of.

How anyone knows is the better story. Cecilia Payne worked it out in her 1925 doctoral thesis, from the spectral lines in sunlight, and concluded the Sun was overwhelmingly hydrogen. The prevailing view was that stars had roughly the composition of the Earth, and her adviser persuaded her to add a line calling the result almost certainly not real. It was real, he published a version of the same conclusion four years later and is often credited with it, and her thesis has been called the most brilliant PhD ever written in astronomy.

The Sun converts about 600 million tonnes of hydrogen into helium every second, losing around four million tonnes of mass as energy in the process, and has been doing so for four and a half billion years with roughly five billion to go. It is also not burning in any chemical sense - a ball of that size made of anything flammable, actually burning, would last a few thousand years, which was a serious nineteenth-century problem until nuclear fusion was understood.