Cook the pasta in a large pot of salted boiling water just until barely al dente according to package instructions (the pasta will finish cooking in the sauce). Reserve ½ cup of the cooking water to thin the sauce later, if necessary. Drain.
Meanwhile, cook the bacon in a large skillet over medium-high heat until crispy, about 7-8 minutes. Transfer the bacon to a paper towel-lined plate to drain, reserving 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 browned on both sides and juices run clear, about 5-7 minutes per side. Remove the chicken to a cutting board, let rest for 5 minutes, and then slice into thin strips.
Wipe the skillet clean to make the sauce. In the skillet, whisk together heavy cream and sour cream. Season with ½ teaspoon of salt and ¼ teaspoon pepper. Simmer the cream mixture over medium heat, whisking, until it thickens, about 5 minutes. Add the lemon zest, lemon juice and Worcestershire sauce. With the sauce at a gentle simmer over medium heat, add the cooked pasta, the chicken, the bacon, and the peas. Toss to coat in the sauce and cook just until warmed through, about 2 minutes. Stir in reserved pasta water, as necessary, to thin the sauce. Taste and season with additional salt and black pepper, if desired. Garnish with the chives and Parmesan; serve immediately.