Pat the chicken thighs dry and slice them thinly. Season the chicken with 1/2 teaspoon of salt. Heat 3 tablespoons of olive oil in a skillet over medium-high heat, add the chicken, and stir occasionally until the meat is cooked through. Transfer the chicken to a plate and set aside.
Meanwhile, bring a large pot of salted water to a boil. Add the spaghetti and cook until al dente. Drain the spaghetti, reserving 1 cup of pasta water.
Melt 4 tablespoons of butter in a skillet over medium-high heat. Add the sliced garlic and chili powder, and sauté for 30 seconds until fragrant. Then pour in the dry white wine. Reduce the heat to medium and bring the mixture to a simmer. Continue cooking for 2 to 3 minutes, or until the sauce is reduced by half.
Transfer the chicken, spaghetti, and 3/4 cup of pasta water to the skillet. Cook over medium heat, stirring in the lemon zest, lemon juice, and the remaining 4 tablespoons of butter. Continue cooking until the butter melts and the pasta has absorbed the sauce completely. Turn off the heat and stir in 1/4 cup of grated Parmesan cheese. Add the remaining salt to taste.
To serve, garnish with the remaining grated parmesan and chopped parsley on top.