Bring a large pot of well-salted water to a boil over high heat. Meanwhile, trim stems and ribs from chard (save for another use, such as soup, if you like). Cut leaves crosswise into 1/3-in.-wide ribbons. Peel any rubbery outer leaves from radicchio and cut out tough core; discard both. Slice remaining leaves crosswise into 1/3-in.-wide ribbons. Zest lemon and set aside zest. Juice lemon and set aside 3 tbsp. juice.
Heat olive oil in a 12-in. frying pan over medium heat. Add garlic and cook until just translucent, about 2 minutes. Increase heat to medium-high. Add chicken broth, sherry, chard, radicchio, and lemon zest. Turn to coat and cook until chard is just tender to the bite, 2 to 3 minutes. Add cream and half the cheese; stir to combine. Stir in chicken and cook until warmed through. Stir in lemon juice and season with salt and pepper.
Meanwhile, cook pappardelle in boiling water according to package directions. When pasta is cooked, drain and add to frying pan; use tongs to combine. Transfer pasta to a serving bowl, sprinkle with remaining cheese, and serve.
Note: Nutritional analysis is per 1 1/2-cup serving.