Bring a large pot of salted water to a boil and cook the linguine until al dente according to package directions.
Season the chicken breast evenly with sea salt and black pepper.
Heat olive oil in a large skillet over medium-high heat and sear the chicken until golden and cooked through, about 5-6 minutes per side.
Remove the chicken from the pan and let it rest for 5 minutes before slicing into thin strips.
In the same skillet, add the garlic and cherry tomatoes, sautéing for 3-4 minutes until the tomatoes begin to blister and soften.
Drain the pasta, reserving two tablespoons of the cooking water.
Add the cooked linguine, sliced chicken, and basil pesto to the skillet with the tomatoes.
Toss everything together over low heat, adding the reserved pasta water as needed to create a silky sauce.
Garnish with parmesan cheese and serve immediately.