In a small sauce pan over medium heat add honey and balsamic vinegar. Bring to a boil and simmer until slightly thickened, 10 minutes. Turn off heat; stir in orange zest and oregano. Reserve 1/4 cup for serving.
Meanwhile, trim off both ends of each zucchini. Using a mandoline or vegetable peeler, create long flat noodles by running blade against the length of each zucchini. Season with salt and set aside.
Preheat grill on medium-high. Drizzle chicken with olive oil and season with salt and pepper. Place chicken on grill and cook for 4 minutes on each side. Brush glaze onto chicken and cook until lightly charred all over and internal temperature reaches 165 degrees F; 2 to 3 minutes. Transfer to a clean plate and cover loosely with foil.
Bring an 8-quart stock pot of water to a boil and generously season with salt. Cook zucchini until al dente, 2 to 3 minutes, and drain. Slice chicken against the grain and serve over zucchini noodles. Drizzle balsamic-honey glaze and sprinkle sea salt. Serve immediately.
Judy Kim is a NYC-based food stylist, recipe developer, and photographer. She also writes recipes for her website The Judy Lab.