Cook the pasta in a large pot of salted boiling water according to package directions until al dente; drain and set aside.
Heat a large high-sided skillet over medium-high heat and add enough olive oil to coat the bottom.
Add the diced chicken to the hot skillet, season generously with kosher salt and freshly ground black pepper, and cook for about 4–6 minutes, stirring and flipping frequently for even browning.
When the chicken is about halfway cooked, add the minced garlic and cook, stirring nearly constantly, for about 1 minute until fragrant.
Add the butter and lemon juice to the skillet and stir continuously until the butter melts and the chicken is cooked through, about 4–5 more minutes.
Toss the cooked pasta into the skillet with the chicken and sauce, and stir well to coat evenly.
Stir in the finely minced parsley, then sprinkle with freshly shaved Parmesan; stir to combine or leave on top when serving, as desired.
Taste and adjust seasoning with additional salt and pepper if needed, then serve warm.