Preheat oven to 425 degrees Fahrenheit. Place chicken on a baking sheet; season with half a teaspoon salt and pepper. Rub two tablespoons oil over chicken; roast on the middle rack for 15 to 20 minutes or until internal temperature reaches 160 degrees Fahrenheit. Set aside.

Prepare the onion jam. Meanwhile, heat a large skillet over medium heat. Add remaining one-third cup oil. When oil begins to shimmer, add onions, stirring to break them up; cook until golden, 20 minutes. Add honey; increase heat to medium-high, and stir until honey melts, three to five minutes.

Add garlic; cook until fragrant, one minute. Deglaze pan with balsamic vinegar, scraping up any stuck-on bits.

Reduce heat to medium, season with remaining salt, and add boiling water. Give everything a nice stir; cook until thickened, three to five minutes. Nestle chicken breast over the bed of melt-in-your-mouth onions. Spoon onion jam over the chicken. Heat through and serve.