Heat oil in a 10-inch wok or skillet over medium-high heat until shimmering.
Add curry paste and cook, stirring constantly and pressing curry paste against bottom of pan until fragrant, about 30 seconds.
Add green beans and increase heat to high.
Cook, stirring and tossing constantly until beans are just beginning to turn tender-crisp, about 2-3 minutes.
Add chicken, 2 teaspoons fish sauce, sugar, and oyster sauce. Stir to combine.
Cook until beans are tender-crisp and chicken is barely cooked through, about 2-3 minutes longer.
Taste sauce and add more fish sauce if desired.
Thin with water until sauce barely coats all the meat and vegetables but is not soupy.
Transfer to a serving platter and serve with jasmine rice.
