Heat a grill pan over medium-high heat and rub the chicken cutlets with the oil, salt and black pepper.
Grill the chicken for 4 to 6 minutes per side until marked and the thickest part reaches 165°F.
Rest the chicken for 5 minutes, slice it across the grain and toast the bread until crisp.
Spread the toast with mayonnaise and build the first layer with chicken, avocado and lettuce.
Add a second toast slice, mayonnaise-side up, followed by bacon, tomato and more lettuce.
Close with the final toast, secure each club with 4 picks and cut it into 4 triangles.