Bring the chicken stock and kosher salt to a rolling boil in a large stockpot over medium heat.
Stir in the long-grain white rice, cover the pot, reduce heat to medium-low, and simmer until the rice has absorbed the broth and is tender, about 20 minutes.
While the rice cooks, combine 1 cup cilantro, 1/3 cup lime juice, 2 tablespoons olive oil, and the minced garlic in a blender or food processor; pulse until just blended.
When the rice is done, remove the pot from heat and stir in the cilantro-lime mixture and 1 teaspoon lime zest until evenly combined.
Fluff the rice with a fork and garnish with the chopped cilantro and remaining lime zest, then serve.