Place the chicken pieces into the slow cooker. Season with salt and pepper. Spread the pesto over the top of the chicken and arrange the butter on top. Cook for 2 to 3 hours on high or 3 to 4 hours on low.
Once the chicken is cooked, remove to chicken to a bowl and allow it to rest for 15 minutes. Reserve the liquids in the bottom of the slow cooker. Cook and drain the pasta. Use two forks to shred the chicken.
Return the shredded chicken to the slow cooker. Stir cheeses into the chicken. Cover the slow cooker and heat on low for 15 to 30 minutes to melt the cheeses. Stir together once cheeses haves softened.