Place the potatoes and carrots into a large pot and fill with enough water to cover. Bring to the boil and cook until potatoes are tender enough to pierce with a fork, 8 to 10 minutes. Drain and rinse under cold water to cool. Set aside.
Heat the olive oil in a large frying pan over medium heat. Add the onion; cook and stir until tender and light brown, about 10 minutes. Set aside to cool.
In a large bowl, combine the potatoes, carrots, chicken, eggs and pickles. In a separate bowl, whisk together the onion, pickle juice and mayonnaise.
Season with salt and pepper. Pour over the potato mixture and stir gently to coat. Adjust the amounts of mayonnaise, salt and pepper if desired. Gently stir in beetroot last. Refrigerate for at least 1 hour to blend flavours before serving.