Is it normal for best friends to become a couple?

That is very common, yes.

I've seen this happen several times, and while I'm happy for the people who experienced it, I don't think it's a very good basis for a marriage or other permanent relationship, because it suggests an absence of sexual chemistry.

If you have good chemistry with someone, it becomes clear pretty much right away that you want to have sex. At a minimum you both have an urge to make out when you are close. Without this you'll have sex less often as the relationship matures, and will need to struggle to sustain that "magic ratio" of 5 good interactions to 1 bad. The magic ratio is real, and if you hold to it you may find that what seem like nasty fights end quickly and are forgotten by the end of the day. This comes far more easily if you make out pretty much every time you are alone together. That might not be what your relationship is like, if you are mainly bros but after a while you catch feelings for each other. At least I haven't seen it.