Preheat a sauté pan over medium-high heat. Add the butter and sauté the chicken strips until browned. Add garlic and thyme leaves and cook for another minute. Add the cream and reduce the heat to a simmer. Simmer the cream and chicken while you cook the pasta.
Drop the fettuccine into the stockpot of water and cook according to the package directions. When the pasta is ready, add the Parmesan cheese and peas to the sauté pan and stir them into the cream to combine. Season to taste with salt and lots of freshly ground black pepper.
Using tongs, transfer the pasta from the stockpot to the sauté pan, bringing a little of the pasta water along with the pasta. Swirl everything together and serve.
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