Bring a large pot of salted water to a boil and cook the linguine until al dente, reserving a small amount of pasta water before draining.
Season the chicken breast evenly with the sea salt and black pepper on both sides.
Heat the olive oil in a large skillet over medium-high heat and sear the chicken until golden brown and cooked through, about 5 to 6 minutes per side.
Transfer the chicken to a cutting board, allow it to rest for 5 minutes to keep it juicy, then slice into thin strips.
In the same skillet, add the minced garlic and chopped sun-dried tomatoes, sautéing for 1 minute until the garlic is aromatic.
Add the cooked linguine and baby spinach to the skillet, tossing gently until the spinach begins to wilt from the residual heat.
Stir in the basil pesto and lemon juice, adding a splash of the reserved pasta water if needed to create a smooth, glossy coating.
Fold the sliced chicken back into the pasta mixture and serve immediately.