Adjust rack to middle position and preheat oven to 425 degrees F (220 degrees C).
Halve Fingerling Potato (to taste) lengthwise. Toss on a baking sheet with a drizzle of Olive Oil (to taste) and a pinch of Salt and Pepper (to taste). Roast in oven until tender and lightly browned, 20-25 minutes total.
Once potatoes have roasted for 10 minutes, remove sheet from oven and give them a toss, pushing toward one side. On the other side of the same sheet, toss Green Beans (to taste) with a drizzle of Olive Oil (to taste) and a pinch of Salt and Pepper (to taste). Return sheet to oven and roast until potatoes are done and green beans are lightly crisped, about 10 minutes. Once done rest for 10 additional minutes.
Halve Shallot (1). Finely mince one half and save the other half for another use.
Heat a drizzle of Olive Oil (to taste) in a large pan over medium-high heat. Pat Boneless, Skinless Chicken Breast (4) dry with a paper towel, then season all over with Salt and Pepper (to taste). Add to pan and cook until no longer pink in center, 4-5 minutes per side. Remove from pan and set aside.
Lower heat under same pan to medium and add shallot, Fresh Thyme (to taste) and a drizzle of Olive Oil (to taste). Cook, tossing until softened, 2-3 minutes. Stir in Apricot Jam (to taste) and Balsamic Vinegar (1 tablespoon). Simmer until syrupy, about 1 minute. Stir in Water (1 tablespoon) and Chicken Broth Concentrate (1 tablespoon). Simmer until thickened, about 3 minutes. Remove pan from heat, add Butter (1 tablespoon) and stir to melt.
Give the sauce a taste and add more vinegar if you prefer a tangier flavor. Season with Salt and Pepper (to taste). Plate chicken, green beans and potatoes. Drizze sauce over chicken and serve.