Whether or not there are infinitely many commensurability classes of nonarithmetic lattices in SU(n, 1) - or any at all for n > 3 - remains a major open problem. One way to show that SL(2; R) has infinitely many is via Schwartzian triangle groups: Takeuchi proved that only finitely many are arithmetic, the key step being a finiteness result in the Galois theory of fields of cosines. Mostow´s finite list of nonarithmetic lattices in SU(2, 1) are a generalization of triangle groups, and the difficult work is proving that his examples act discretely and with finite covolume. It is unknown if infinitely many of these so-called complex hyperbolic triangle groups are indeed lattices, and I will prove that only finitely many can be nonuniform arithmetic lattices, thus giving an infinite list of candidate nonarithmetic lattices. Given time, I will also discuss the cocompact setting. As with Takeuchi, the primary tool is Galois theory.