Cut the chicken breasts into 1-inch pieces.
Add the flour to a sealable plastic bag then add the chicken and seal the bag. Shake the bag until the chicken is coated all over.
Whisk the eggs in a shallow dish. Add the breadcrumbs to a second shallow dish.
Remove each piece of chicken from the bag, shake off any excess flour, then dip it in the eggs then breadcrumbs. Repeat the coating process with all of the chicken pieces.
Heat at least 2 inches of oil in a large heavy-bottomed stock pot set over medium-high heat. Once the oil reaches 360°F, add a portion of the chicken and cook, flipping occasionally, until golden brown and cooked through, about 2 minutes.
Using a slotted spoon, transfer the chicken to the paper towel-lined baking sheet then repeat the cooking process with the remaining chicken, returning the oil to 360°F between batches.
Transfer all of the chicken to a large bowl then stir in the red and green peppers and pineapple.