Cut each focaccia round in half horizontally. Using kitchen scissors, snip any large pieces of chutney. Spread the bottom halves of 2 of the rounds with chutney; set aside. In a small bowl stir together the mayonnaise and pesto; spread over the bottom halves of the remaining focaccia rounds.
Arrange the ham on the chutney-spread focaccia. Arrange chicken on the pesto-spread focaccia. Top each with sliced tomato or red onion and cover with focaccia tops. Cut each round into sixteen 2-inch-wide wedges, secure each sandwich with a decorative pick, and arrange on serving platters. Cover and chill up to 4 hours before serving. Makes 64 appetizers.