Heat the olive oil and 1 tablespoon of butter in a large skillet or sauté pan over medium-high heat.
Season the chicken pieces with salt and pepper, then brown in the pan for 5-7 minutes until golden on all sides. Remove the chicken from the pan and set aside.
Add the remaining tablespoon of butter to the same skillet. Add the sliced leeks and garlic, sautéing for 8-10 minutes over medium heat until the leeks are soft and translucent.
Pour in the white wine to deglaze the pan, scraping the bottom with a wooden spoon to release any browned bits.
Return the chicken to the pan and add the heavy cream and dried thyme.
Reduce the heat to medium-low and simmer gently for 12-15 minutes until the chicken is fully cooked and the sauce has thickened enough to coat the back of a spoon.
Adjust seasoning with salt and pepper to taste, garnish with fresh parsley, and serve immediately.