Store leftover salad and dressing separately. The beets will bleed, discoloring the cucumber and carrot, so if storing, keep the beets separate until serving. Toss before eating.
I highly recommend the "dry poaching" method for cooking your chicken, recommended by
The Kitchn. I've included the recipe in this post, but I highly recommend visiting The Kitchn - their site is full of great resources and recipes.