Whisk balsamic vinegar, honey, and minced garlic in a small bowl to create the glaze.
Season chicken breasts with salt, pepper, and dried oregano on both sides.
Heat olive oil in a large skillet over medium-high heat.
Add chicken to the skillet and cook for 6-8 minutes per side until the internal temperature reaches 165°F (74°C).
Remove chicken from the skillet and set aside.
Add asparagus to the same skillet and cook for 3-5 minutes until tender-crisp.
Pour the balsamic glaze into the skillet and simmer for 2-3 minutes until thickened.
Return chicken to the skillet, toss with the glaze and asparagus, and serve immediately.