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1
Chop the zucchini into 1/2-inch-wide half moons (cut these in half if the zucchini is very large) and set them aside. Cut the chicken into even, bite-sized chunks about 1-inch long and set aside. Open the cans of coconut milk and set them to the side.
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2
Heat a drizzle of vegetable oil in a 4-quart (or larger) Dutch oven or heavy pot set over medium-high heat, and when the oil is hot, add the curry paste. (For a fully tongue-tingling experience, use the full 4-ounce can. If you have a lower tolerance for heat, use half the can.) Fry the paste for 2 minutes, stirring frequently. This will be quite pungent, so turn on the fan!
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3
Scoop the thickened coconut solids out of both cans of coconut milk, leaving the watery milk below. Fry this for about 2 minutes with the curry paste too, until the oil starts to separate out, forming beads on top of the curry paste. Add the chicken pieces and saute for about 1 minute.
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4
Add the rest of the coconut milk. Reduce the heat to medium low and simmer until the chicken is cooked through - about 10 minutes.
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5
When the chicken is done, add the zucchini and simmer just until they're tender. Taste and adjust seasonings with sugar, and soy sauce until it is balanced enough for your tastes.
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6
Serve with rice or rice noodles. This keeps well, freezes well, and does great made the night before and heated up the next day.
