Cook the linguine according to package instructions until al dente. Drain and set aside, reserving 1/2 cup of pasta water.
In a large skillet, heat the olive oil over medium heat. Add the chicken pieces and season with salt and pepper. Cook until the chicken is browned and cooked through, about 5-7 minutes. Remove the chicken from the skillet and set aside.
In the same skillet, add the butter and minced garlic. Sauté for about 1 minute until fragrant, being careful not to burn the garlic.
Pour in the heavy cream and bring to a gentle simmer. Stir in the Italian seasoning, then gradually add the cheddar and Parmesan cheese, stirring until melted and smooth.
Return the cooked chicken to the skillet and add the drained linguine. Toss everything together, adding reserved pasta water a little at a time until the sauce reaches your desired consistency.
Taste and adjust seasoning with more salt and pepper if needed.
Serve immediately, garnished with chopped parsley.