In a large bowl or resealable plastic bag, combine the California olive oil, minced garlic, Meyer lemon juice, and crushed red pepper flakes. Add the chicken strips and toss until every piece is well coated. Cover and refrigerate for at least 30 minutes, or overnight for deeper flavor.

In a large bowl, beat the softened butter with garlic, lemon zest and juice, Dijon mustard, paprika, red pepper flakes, chives, salt, and black pepper until smooth and fully blended. Put half of the butter in a separate container to brush over the cooked skewers, and leave the rest for basting while grilling.

Thread the marinated chicken strips evenly onto skewers, leaving a little space between pieces so the heat can circulate and cook them without steaming.

Preheat a grill to medium-high heat, about 400 to 450 degrees F. Place the skewers on the grate and grill for 4 to 5 minutes per side, turning once and basting with the basting butter. Cook until the chicken is no longer pink in the center and reaches an internal temperature of 165 degrees F.

Remove the skewers from the grill and transfer them to a platter. Brush generously with the reserved cowboy butter and finish with extra chopped chives before serving.