In a medium pot, combine chicken and enough water to cover by one inch; season with salt. Bring to a simmer over medium-high heat, then reduce heat to a low simmer and cook chicken until cooked through, 18 to 20 minutes. Transfer chicken to a plate and let sit until cool enough to handle. Slice thinly.

Whisk together orange juice, oil, and juice of half a lemon. Season with salt and pepper.

Toss apple slices with remaining lemon juice to prevent browning.

Arrange beets on a large platter. Top with greens, chicken, apples, and pomegranate seeds. Drizzle with orange dressing.