Combine all ingredients in a small saucepan over medium low heat. Cook until the garlic and green onions begin to brown, then remove from heat and let cool completely. This can be stored in the fridge and made a few days ahead of time.
Season the chicken with the brown sugar, salt and pepper. Heat a large skillet over medium-high heat and add olive oil. Add the chicken and sear until golden brown on all sides. Cook for 6 to 7 minutes, until cooked through. Remove from heat and set aside.
Cook the soba noodles as directed. When finished cooking, rinse the noodles under cold water and add them to a large bowl. Toss with the soy sauce, vinegar, brown sugar and sesame oil. Add in the chicken, cucumber, radish and cilantro, tossing well. Serve with drizzles of the chili oil. This is also delicious once it sits in the fridge for a few hours.