Bring a large pot of salted water to a rolling boil and cook the fettuccine according to package directions, about 1–2 minutes less than stated 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 the avocado oil in a large skillet over medium-high heat until shimmering. Add the chicken in a single layer and let cook undisturbed 3–4 minutes until golden on one side. Stir and continue cooking 4–5 minutes more until cooked through and richly browned. Transfer the chicken to a bowl and set aside.
Reduce heat to medium, add the minced garlic to the skillet, and sauté 1–2 minutes until fragrant but not browned.
Pour in the two cans of full-fat coconut milk and bring to a gentle boil. Stir in the rice vinegar, sea salt, and ground nutmeg. Let simmer at a gentle boil 3–5 minutes to slightly reduce and meld flavors.
Return the cooked chicken and drained fettuccine to the skillet. Toss well to coat; the sauce will appear thin at first but will thicken as the noodles absorb it over about 10 minutes. Cook, stirring occasionally, until the sauce reaches your desired consistency.
Serve immediately. If desired, offer lemon wedges on the side to finish with a squeeze of fresh lemon juice.
