Cook orzo according to package directions. Drain, rinse with cold water and set aside.
Combine olive oil, vinegar, oregano, garlic, salt and pepper in a small mason jar. Shake vigorously to combine.
Add cooked orzo, goat cheese, cucumber, tomatoes and chickpeas to a large bowl and stir to combine. Drizzle 2/3 of oregano vinaigrette over orzo mixture and stir to combine. Chill for at least 1 hour. Stir before serving and add remaining vinaigrette if desired.