Why was the early universe's entropy low?

[Thecla]

I have read that the early universe had a very low entropy. I don't understand why. A giant ball of plasma at billions of degrees K with particles moving in all directions. It seems like the definition of total disorder. Why is the entropy considered low?

 

[mfb]

Without gravity it would be a high entropy state, but gravitational attraction makes localized matter concentrations a higher entropy state in the later universe. These mass concentrations lead to a higher temperature relative to a uniform gas distribution.