In a medium saucepan, add olive oil, minced garlic, and ginger. Sauté over medium heat for 2-3 minutes and add honey, lemon juice, lemon zest, apple cider vinegar, soy sauce, and cornstarch. Bring to a boil and reduce to a simmer. Let simmer and thicken while cooking chicken.
Cut the chicken into bite sized pieces and add to a medium skillet. Cook about 4-5 minutes until no longer pink in center and the outside is starting to brown. Add the sauce to the chicken and toss to coat.