Do two hydrogens with same spin make H_2 ?

[spocchio]

As I know from the laws of chemistry,to form H_2 the H atoms must have opposite spin.
What if they have the same spin?
I mean, can an H atom rotate to swap his spin (i'm not expert of the dynamics of spin), or there is no way to couple them?
In the case I have a gas of H with all of them polarized in the same direction is the formation of H_2 possible?

 

[chemisttree]

What spin are you talking about? Electron spin?