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In a pot over medium-high heat, cook chicken in olive oil. Season with salt and pepper to taste.
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When cooked through, remove chicken from pot and place on a cutting board.
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Add onion, carrots, celery and garlic to the same pot and reduce heat to medium. Stir frequently until vegetables are soft.
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Cut up cooked chicken into roughly 1” pieces and return to pot with vegetables.
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Sprinkle the flour over the chicken and vegetables and toss to coat.
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While continually stirring, add milk in a steady stream.
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Add remaining seasonings, salt to taste, and cook until thickened and just beginning to bubble.
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Turn off the heat and set aside.