Slice the chicken breast into thin strips 3 to 4 inches long; this is easier to do if the chicken is placed in the freezer for 20 minutes before slicing. You should have about 40 slices (count out and set aside roughly half as many wooden skewers as you have slices of chicken). In a medium bowl, mix the 1/2 cup tamari, the orange juice, lime juice, and two of the garlic cloves.
Add the chicken slices. Cover the bowl and refrigerate for at least one hour and up to overnight.
Before you are ready to grill the chicken, soak the wooden skewers in water for at least 20 minutes.
Meanwhile, in a blender or the work bowl of a food processor, place the vinegar, almond butter, honey, ginger, sesame oil, 1 teaspoon tamari, and remaining garlic clove. Blend or process until smooth. Set aside until ready to serve.
If using a gas or charcoal grill, spray the grill with olive oil and prepare a medium-hot grill. If using a grill pan, spray it with olive oil and heat over medium- high heat.
Pat the chicken slices dry, and thread two slices onto each skewer. Grill for two to three minutes per side. Arrange the hot skewers on a platter and either drizzle the sauce over or serve the sauce in a bowl alongside the skewers.