Bring a large pot of salted water to a boil and cook the linguine according to package directions until al dente.
While the pasta cooks, season the chicken breast on both sides with sea salt and black pepper.
Heat the olive oil in a large skillet over medium-high heat and sear the chicken until golden brown and cooked through, approximately 5-6 minutes per side.
Remove the chicken from the skillet, let it rest for 3 minutes, then slice into thin strips.
In the same skillet, add the cherry tomatoes and minced garlic, sautéing for 3-4 minutes until the tomatoes begin to blister and soften.
Drain the pasta, reserving 2 tablespoons of the starchy cooking water.
Add the cooked pasta, sliced chicken, basil pesto, and reserved pasta water to the skillet with the tomatoes.
Toss all ingredients together over low heat until the sauce is creamy and everything is well-coated.
Serve immediately garnished with the grated parmesan cheese.