Heat grill to medium-high. Once it is hot, clean the grill grate with a wire brush. Just before grilling, oil the grill grate.
Soak 8 skewers in water for at least 15 minutes.
Toss the chicken, plums, garlic, oil, ½ teaspoon salt, and ¼ teaspoon pepper in a medium bowl. Thread onto the skewers. Grill, turning occasionally, until the chicken is cooked through, 8 to 10 minutes. Sprinkle with the oregano.