For chutney:
Blend first 5 ingredients and 2 tablespoons yogurt in blender or processor. Blend in more yogurt if necessary to make smooth paste. (Chutney can be made 1 day ahead. Cover and refrigerate.)
For chicken:
Whisk first 6 ingredients in large bowl to blend. Add chicken and toss to coat. Cover and refrigerate at least 2 hours and up to 12 hours.
Preheat broiler. Thread 1 chicken piece on each skewer. Cover exposed part of skewers with foil. Broil chicken until cooked through, turning occasionally, about 8 minutes. Arrange lettuce and cucumber on platter. Top with chicken. Squeeze lime over. Serve chicken with Cilantro-Mint Chutney.