In a serving bowl, combine the olives, capers, gherkins, onion, celery, eggs, sugar, mayonnaise and lemon juice. Stir to blend well.
Boil the chicken until well cooked, about 20 minutes. In a separate saucepan, boil the potatoes for 10 minutes, then add the peas to the potatoes and boil another 5 minutes. Drain the peas and potatoes.
Shred or cube the chicken and add it and the peas and potatoes to the mayonnaise mixture. Toss, taste and add salt and pepper as needed. Serve warm.