In a large pot of boiling water, cook pasta until al dente. Drain pasta and return to pot.
While pasta is cooking, heat oil in a large pan over medium heat. Add onion; cook, stirring occasionally, until onion begins to brown, 1 to 2 minutes. Add chicken. Cook chicken uncovered until it is done, about 8 minutes.
In a small saucepan of boiling water, add frozen peas. Cook, stirring occasionally, until peas are warmed through and tender, 2 to 3 minutes. Drain well and return peas to the pot. Add tomatoes and cook on medium-low heat for 45 seconds. Remove from heat.
To pasta in pot, add the pesto, chicken, onions, peas, and tomatoes. Mix well and keep warm. Serve immediately, sprinkled with Parmesan.
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