Spread the basil pesto over both slices of bread. Layer the chicken and cheese onto one slice and assemble the sandwich. Butter both sides.
In a medium non-stick pan over medium-high heat, grill the sandwich for 2 to 3 minutes until the bottom is golden brown. Flip and continue to grill until the cheese is melted.
Remove from heat and allow the sandwich to cool to room temperature.
Once cooled, slice it in half and pack it inside a lunch container.
If adding veggies or fruit, be sure to pack them in a separate compartment or container.
Close the lunchbox and place it in the lunch bag with an ice pack.