Add the rice to a fine-mesh sieve and rinse under cool water until the water runs mostly clear. Drain well.
Pour the water into a medium saucepan and season with the salt. Bring to a gentle boil over medium-high heat.
Stir in the rice, the fresh lime juice, and about half of the lime zest.
Return to a gentle boil, then immediately reduce the heat to low and cover with a tight-fitting lid.
Cook for about 20 minutes, or until the rice is tender and the liquid has been absorbed.
Remove the pan from the heat and let the rice rest, covered, for 5 minutes.
Uncover and gently fluff the rice with a fork.
Let the rice cool for about 5 minutes, then stir in the chopped cilantro and the remaining lime zest, if desired. Taste and season with additional salt, if needed, then serve warm.
