In a large saucepan, combine the nectarines, sugar, lemon juice and thyme. Bring the mixture to a boil and reduce to a simmer. Cook the mixture, stirring frequently, until it turns into a thick chunky jam, about 20 minutes. Remove the thyme and let the jam cool.
To make the sandwiches, spread the cut sides of the focaccia with jam and mustard. Arrange the chicken on the bottom sides of the focaccia and top with arugula, Taleggio and the remaining focaccia.