Crock pot method: Place about 1 tablespoonful of pesto in the bottom of the crock pot and spread evenly over the bottom. Place the chicken breasts in an even layer on top. Spread the remaining pesto over the chicken pieces. Cook the chicken on the medium setting for 3 hours or until the pieces are no longer pink in the middle (use a meat thermometer to check that the internal temperature of the chicken has reached 165 F if need be). The pesto will lose its color a bit with this long cooking, but not its flavor.
Stove top method. Coat the chicken breasts with pesto as above. In a skillet on medium heat, cook the chicken pieces uncovered on medium heat for about 5 minutes or until they are slightly browned,, then turn the pieces and cook the other side. Cover the skillet and finish cooking, about 5 minutes more. Test the chicken for doneness.
Oven method. Preheat the oven to 375 degrees F. Coat the chicken breasts as above and place in a baking dish. Cover the baking dish with aluminum foil (or use a baking dish with a tight-fitting lid) and bake the chicken for 25-30 minutes, just until chicken is firm and cooked through. Remove the lid during the last five minutes or so if you want the chicken to brown a bit.
Allow the chicken breasts to cool enough to handle, and slice crosswise.
To assemble the dish. Arrange cooked pasta on individual plates. Stir 1-2 tablespoons of pesto into each serving of pasta. Distribute the cooked vegetables over the top. Place one sliced chicken breast on top of each serving.