Preheat oven to 450 degrees. Line a baking sheet with foil or parchment paper, brush with oil, and set aside. Soak 24 bamboo skewers in water for at least 30 minutes to prevent burning.
Rinse chicken breasts with cold water and pat dry, Cut each piece of chicken into 3/4 inch chunks.
In a medium bowl, combine mustard and shallot. In another medium bowl, combine bread crumbs and parsley. Toss chicken pieces in mustard mixture to coat, then dredge in parslied bread crumbs. Thread 2 or 3 chunks onto end of each skewer and place on prepared baking sheet. Bake until chicken is cooked through but still juicy, 5-7 minutes. Serve warm.