In a mixing bowl combine the dried oregano, honey, minced garlic, Sriracha, rice vinegar, olive oil, soy sauce, and salt; whisk until smooth and evenly combined.
Transfer the marinade to a resealable plastic bag.
Trim excess fat and cartilage from the chicken breasts, then pound or slice them to an even thickness of about 1/2 inch.
Add the chicken to the bag with the marinade, seal, and move the chicken around until fully coated.
Refrigerate the sealed bag and marinate the chicken for 1 hour.
Remove the chicken from the marinade and place directly on a preheated grill; cook until done, about 10 minutes total depending on thickness, flipping once.