Process pine nuts and garlic in a food processor until the texture of coarse sand; about 30 seconds.
Add basil and parmesan cheese, process until a paste forms. Add 1/3 cup olive oil. Process to incorporate; about 10 seconds.
Cook pasta according to package directions. Reserve 1/2 cup of pasta cooking liquid. Drain pasta and rinse with cold water until the pasta is room temperature.
Heat an electric griddle, or large nonstick skillet. Coat with non-stick spray and cook chicken over medium heat until golden on both sides, about 8 minutes total.
Place pasta in a large bowl. Add tomatoes, 1/4 cup pesto, pine nuts, lemon juice and zest. Toss to coat. Add pasta cooking liquid, a few tablespoons at a time, to coat pasta and thin the pesto sauce. Add chicken, toss and serve.
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