Season chicken on both sides with garlic salt. Preheat skillet to a medium/high and cook chicken until golden brown. Poke with a knife to see if the chicken is cooked through. Let the chicken rest for about 5 minutes and dice it into one inch cubes.
Melt the butter with oil in a large saucepan over medium heat. Add onion, celery, carrots and garlic. Cook, stirring occasionally, until the veggies softens. Whisk in the flour and cook for about 1 minute.