Preheat a barbecue to medium-high. In a large bowl, mix together oil, lemon zest, lemon juice, salt and pepper. Add mushrooms and capsicums and toss well. Add onion and toss gently.
Using six 25 cm (10 inch) skewers, thread mushrooms onto one skewer, reserving mixture in bowl. Thread capsicums in alternating colors onto two more skewers, and onion on a fourth skewer.
Add chicken to mixture remaining in the bowl and toss well. Thread chicken onto final two skewers.
Place all skewers on the barbecue and cook 15 cm (6 inches) from the heat for 5 minutes, turning chicken and vegetables as they colour, until cooked through.
Remove chicken and vegetables from skewers and arrange on a serving platter.