Cook the pasta in a large pot of salted boiling water just until barely al dente according to package instructions (about 1 minute less than directed). The pasta will finish cooking in the sauce. Reserve ½ cup of the starchy cooking water before draining. Drain the pasta and set aside.
Meanwhile, cook the bacon in a large skillet or Dutch oven over medium-high heat until crispy, about 7 to 8 minutes. Transfer the bacon to a paper towel-lined plate using a slotted spoon, leaving the drippings in the pan.
Season the chicken with salt and pepper on both sides. Cook the chicken in the bacon drippings over medium-high heat until golden brown and cooked through, about 5 to 7 minutes per side. Remove the chicken to a cutting board, let it rest for 5 minutes, and then slice into thin strips.
Wipe the skillet clean with a paper towel. Whisk together the heavy cream and sour cream in the skillet. Season with ½ teaspoon salt and ¼ teaspoon pepper. Simmer the cream mixture over medium heat, whisking occasionally, until it thickens slightly, about 5 minutes. Stir in the lemon zest, lemon juice, and Worcestershire sauce.
With the sauce at a gentle simmer, add the cooked pasta, sliced chicken, crispy bacon, and frozen peas. Toss to coat everything in the sauce and cook just until warmed through, about 2 minutes. Stir in reserved pasta water, a couple of tablespoons at a time, as needed to thin the sauce to your desired consistency.
Taste and season with additional salt and pepper, if desired. Garnish with chives and freshly grated Parmesan cheese. Serve immediately.