Place rice in a fine mesh sieve and rinse under cold water, stirring with your fingers to move the rice around, until the water runs clear, about 1 minute.
In a small pot, combine all the coconut milk, all the chicken stock, and lime juice and place over medium high-heat. Immediately when the liquid starts to bubble around the edges at a low simmer, add the rice and Kosher salt. Stir and cover the pot tightly (not opening the lid the entire time), then reduce heat to low, and cook until tender, 15 minutes. Turn off heat and let sit, still covered, for 10 minutes. (TIP: It’s important not to remove the lid during these 25 minutes of cooking and resting).
Fluff rice with a fork and stir in lime zest and cilantro. Taste and season with additional lime juice and salt, if needed. Serve immediately.
Notes
Coconut rice can be cooled completely and then stored in an airtight container in the refrigerator for up to 3 days. Must be reheated until warmed through, this dish will not be good served cold or room temperature.