Rub chicken breasts with about 3 tablespoons of jerk seasoning and refrigerate until ready to use.
Heat oil in a skillet over medium heat. Add onion and peppers and saute until nearly tender, about 3 minutes. Combine Alfredo sauce with remaining 2 tablespoons jerk seasoning and 1 ounce pineapple juice. Stir mixture into the skillet, reduce heat to low, and let simmer.
In the meantime, fill a large pot with lightly salted water and bring to a rolling boil. Add fettuccine to the pot of boiling water and cook until tender yet firm to the bite, about 8 minutes.
Preheat an outdoor grill for medium-high heat and lightly oil the grate.
Add garlic and pineapple chunks to the sauce. Increase heat and bring to a boil. Return heat to low and simmer, stirring occasionally, until flavors blend as desired.
Drain pasta and keep warm. Grill the chicken until the juices run clear, 5 to 7 minutes per side. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C). Slice into strips.
Plate the pasta and chicken and cover with the sauce.
