Heat the oil in a medium non-stick skillet over medium heat. When hot, add onions and lightly season with salt. Cook the onion for 20 minutes, stirring frequently to prevent burning. Remove from heat and toss with thyme. Transfer to a bowl and place in the refrigerator to cool. When cool, add ground chicken to onions and form into 4 patties. Season the patties with salt. Heat a large non-stick skillet over medium-high heat. When hot, add the patties and cook until browned on both sides and cooked through. Serve immediately.