Prepare the pesto: in a food processor combine basil, pine nuts, garlic, and Parmesan (do not add the olive oil yet).
Pulse until ingredients are finely chopped, then with the processor running slowly pour in the 1/2 cup oil until the mixture is combined and smooth; add more oil for a thinner sauce and season with sea salt to taste.
Bring a large pot of salted water to a boil and cook the pasta according to package instructions until al dente (about 1–2 minutes less than package time), then drain in a colander.
While pasta cooks, cut the chicken thighs into bite-sized pieces.
Heat 1 tablespoon avocado oil in a large skillet over medium-high heat. Add the chicken and cook, stirring occasionally, until cooked through and lightly browned, about 6–8 minutes.
Add the drained pasta and prepared pesto to the skillet with the cooked chicken and toss over low heat until everything is evenly coated and heated through.
Taste and adjust seasoning with additional sea salt, black pepper, lemon juice or extra Parmesan if desired, then serve immediately.