Many computations of open Gromov-Witten invariants are known for Lagrangian submanifolds fixed by an anti-symplectic involution. I will discuss a computation of these invariants for the Chiang Lagrangian, which is a Lagrangian submanifold in CP^3 that is not fixed by an anti-symplectic involution. Then, I will survey some results concerning this computation such as non-monotonicity of the invariants with degree, periodicity of the sign, and denominators of the invariants which are powers of 2. In addition, I will present the small relative quantum cohomology's computation. This is a joint work with A. Hollands, E. Kosloff, Q. Shu, and J. Solomon.