In a large frying pan over medium-high heat, warm 1 to 2 teaspoons oil until hot but not smoking. Add the sweet potato, season with salt and pepper, and cook, stirring occasionally, until tender and lightly browned, 6 to 8 minutes. Transfer to a plate.
In the same pan over medium-high heat, warm 1 to 2 teaspoons oil until hot but not smoking. Add the onion, season with salt and pepper, and cook, stirring occasionally, until starting to soften, 2 to 3 minutes. Working in batches if needed, add the collard greens and cook, stirring occasionally, until wilted, 3 to 5 minutes.
Stir in the apple cider vinegar and molasses and bring to a boil. Reduce to a simmer and cook until the liquid is thickened slightly, 1 to 2 minutes. Add the sweet potato and toss to combine. Remove from the heat and season to taste with salt and pepper.
While the vegetables cook, prepare the chicken.