Cook the 1 cup long-grain white rice (such as jasmine) according to package directions; keep warm.
Put the ¼ small red onion, thinly sliced, in a small bowl. Drizzle with 2 tablespoons lime juice and a generous pinch kosher salt, toss to coat, and set aside to pickle while you cook.
Heat 2 tablespoons canola oil in a high-sided skillet or large saucepan over medium-low heat. Add 3 tablespoons Thai green curry paste and cook, stirring often, until fragrant, about 3 minutes.
Pour in the 1 14-ounce can coconut milk and ¾ cup water. Whisk to smooth the curry paste into the liquid. Increase heat to medium, stir in 2 tablespoons fish sauce, and simmer gently for 5 minutes.
Add the thinly sliced chicken breast and cook, stirring occasionally, for 1 minute.
Add 1 cup zucchini (sliced into half moons), 1 cup red bell pepper (½-inch chunks), and 1 cup green bell pepper (½-inch chunks). Cook, stirring occasionally, 4–5 minutes, until the vegetables are fork-tender and the chicken is cooked through.
Stir in ½ cup frozen peas and the remaining 4 tablespoons lime juice. Cook just until the peas are heated through.
Serve the curry over the cooked rice. Top with the pickled red onion, ½ cup cilantro leaves (roughly chopped), roasted peanuts, and lime wedges for squeezing.