Preheat the oven to 220ºC/425ºF/gas 7. Unroll the pastry, cut it in half lengthways, then cut each half widthways into 8 equal strips. Flatten the chicken breasts by pounding with your fist until the fat ends are the same thickness as the skinny ends. Place them in a roasting tray, season with sea salt and black pepper, spread over the pesto, then lay 4 overlapping strips of pastry over each breast, tucking them under at the edges. Brush with a little olive oil. Lightly dress the tomato vines in olive oil, season and put into a second tray. Place the chicken tray on the top shelf of the oven with the tomatoes below, and cook for 20 minutes, or until the pastry is golden and the chicken is cooked through.
Meanwhile, line up the beans, trim off just the stalk ends, then cook in a pan of boiling salted water for 7 minutes, or until tender. Remove the chicken to a board with half the tomatoes, squashing the rest in the tray and discarding the vines. Drain and toss in the beans, taste and season to perfection. Slice the chicken at an angle and serve on top of the beans, with the whole tomatoes.