Heat a large skillet over medium heat and add the olive oil. Let it warm up before adding anything.
Add the chicken to the pan in a single layer. Season lightly with salt and pepper. Let it cook without touching it for a few minutes, then stir and cook until mostly done. Remove chicken and set aside.
In the same skillet, add the onion. Cook until soft and slightly golden. Do not rush this part.
Add carrots and celery. Stir and cook for a few minutes until they start to soften.
Add garlic and cook just until fragrant. About 30 seconds.
Pour in the chicken broth and scrape the bottom of the pan to release any stuck bits.
Stir in thyme and bay leaf. Add the chicken back to the skillet. Let everything simmer gently until vegetables are tender.
Reduce heat to low and slowly stir in the milk or half and half. Let it heat through and thicken slightly.
Add frozen peas and stir. Cook for another minute or two.
Taste and adjust salt and pepper as needed. Remove bay leaf.
Turn off heat and let the skillet sit for a minute before serving. It will thicken a bit more as it rests.