In a large bowl, combine first 4 ingredients. Add just enough mayonnaise to moisten. Cover and chill to blend flavors.
Butter 2 slices of bread. Spread enough chicken salad mixture on one of the buttered slices to make a thick sandwich. Cover with remaining top slice. Repeat with remaining slices of bread.
For best tea sandwich results, chill for at least 30 minutes before cutting. Trim off bread crusts and cut into triangles or squares. Keep covered with a moist paper towel or in an airtight container until ready to serve.