Cut vegetables into 3-inch thin strips.
Cut 4 (10-inch) circles of parchment; fold circles in half. Open circles, and brush half with oil. Place a chicken breast on oiled halves: spread with mustard. Top with leek and carrot. Sprinkle with thyme, salt, and pepper. Fold paper over; starting at 1 end, pleat and crimp edges to seal. Place on a baking sheet.
Bake at 450° for 15 minutes or until chicken is done.