Cut pumpkin into quarters. (Microwaving on high 2 min makes this easier.) Scoop out stringy pulp and seeds, then discard. Peel, then chop pumpkin into bite-size chunks. If you like it spicy, leave seeds in jalapeno. If not, discard them. Mince jalapeno.
Pour coconut milk into a large saucepan and set over medium-high heat. Whisk, then add pumpkin and jalapeno. Cut chicken into bite-size pieces. Stir into milk along with remaining ingredients except cilantro. Once boiling, reduce to medium-low. Simmer, uncovered and stirring often, until chicken is cooked through and pumpkin is fork-tender, 15 to 18 min. Stir in cilantro. Delightful over jasmine rice.