Bring a large pot of salted water to a rolling boil and cook the fettuccine according to package directions, removing 1–2 minutes early for al dente. Drain in a colander and set aside.
While the pasta cooks, cut the chicken breasts into bite-sized pieces and season with a pinch of salt.
Heat avocado oil in a large skillet over medium-high heat until shimmering. Add the chicken in a single layer and let cook undisturbed for 3–4 minutes to brown.
Stir the chicken and continue cooking another 4–5 minutes, or until pieces are golden-brown and cooked through. Transfer the chicken to a bowl and return the skillet to the stove.
Add the minced garlic to the skillet and sauté 1–2 minutes over medium heat until fragrant but not burnt.
Pour in the coconut milk and bring the sauce to a gentle boil. Stir in the rice vinegar, sea salt, and nutmeg, and simmer 3–5 minutes until slightly thickened.
Add the cooked chicken and drained fettuccine to the skillet and toss to coat. Simmer together about 10 minutes, stirring occasionally, until the noodles absorb some sauce and the mixture thickens.
Serve immediately. If desired, squeeze fresh lemon over each portion before serving.