In a small bowl or measuring cup, stir together ¼ cup water with the honey, pepper and ½ teaspoon salt; set honey mixture aside.
In a medium bowl, stir together the flour, turmeric and 1 teaspoon salt. Add the chicken and toss until coated.
In a medium (10-inch) nonstick skillet, heat the oil over medium-high. Add the chicken and cook until the turmeric is fragrant and the chicken is golden brown on both sides, 2 to 3 minutes per side.
Add the asparagus, season with salt, stir to combine and cook until crisp-tender, 1 to 2 minutes.
Add the honey mixture and cook, stirring, until the chicken is cooked through and the sauce has thickened, 2 to 3 minutes.
Remove from heat and stir in the vinegar. Season to taste with salt and pepper. Serve with lime squeezed over top, if you like.
