In a large pot bring chicken broth a boil.
Add chicken to broth, cover and simmer under medium heat until cooked.
Remove chicken from pan and cut into bitesize pieces.
Transfer liquids to a container and return pan to stove. Do not wash it.
Add vegetable oil to pot and saute onions, celery and carrots until tender.
Remove vegetables from pot and transfer to chicken's plate. Do not wash pot and return it to stove.
In same pot melt butter and add flour, stir for 1 minute under low heat.
Slowly pour chicken broth whisking constantly, as it cooks the liquids should start to thicken. Add milk and if needed blend mixture (I use a hand held blender) to remove all lumps.
Add salt, black pepper, lime juice and parsley. Stir.
Return chicken and vegetables to pot and for last add frozen peas. Stir.
Cook for 5 more minutes under low heat and it should be ready to serve.
Drizzle olive oil, sprinkle black pepper and enjoy!