In a medium saucepan, combine 1 1/3 cups water and 2/3 cup brown rice. Bring to a boil over high heat. Reduce heat to the lowest setting, stir once, cover, and simmer about 15 minutes, or until the water is absorbed.
While the rice cooks, in a separate saucepan combine 3 cups coconut milk, 1/2 cup coconut palm sugar, 1/8 teaspoon salt, and 1/2 teaspoon cinnamon (if using). Heat over medium, stirring occasionally, until the mixture comes to a gentle simmer and the sugar is dissolved.
Add the cooked rice to the simmering coconut milk mixture. Reduce heat to low and cook, stirring every 2–3 minutes, for about 15 minutes, until the pudding has thickened to your liking.
Remove the pot from the heat and stir in 1 teaspoon vanilla extract and 1/2 cup dark chocolate chips until the chocolate is melted and evenly incorporated.
Serve the pudding warm, or chill in the refrigerator for at least 1 hour and serve cold. If desired, sprinkle a little additional cinnamon on top.