Make a slit in each chicken breast along its length. Open and fill with the pesto. Stretch each bacon rasher with the back of a sharp knife to lengthen, then wrap tightly around the chicken breast to enclose the pesto filling.
Heat the oil in a large heavy-based frying pan and cook the chicken breasts over a medium-high heat for 10–12 minutes until golden and cooked through.
Serve the chicken with seasonal vegetables and new potatoes, if liked.