Gently poached chicken keeps all its moisture without any added fat. Cool cucumber salad on the side makes this one of the lightest dinners you can eat.
Fill a medium saucepan with 6 cups of water, add half the salt, and bring to a gentle simmer over medium heat.
Slide chicken breasts into the simmering water. Reduce heat to low so bubbles barely break the surface. Cover and poach for 12–14 minutes until the internal temperature reaches 165°F.
Lift chicken out and rest on a cutting board for 5 minutes to lock in moisture. Slice thinly with a sharp knife.
While chicken rests, slice the cucumber thinly and chop the green onions and dill. Place all in a mixing bowl.
Add remaining salt, black pepper, vinegar, and olive oil to the salad. Toss well and let stand for 3 minutes to meld flavors.
Serve sliced chicken atop or beside the dressed cucumber salad. Sprinkle extra dill if desired.