In a small bowl or measuring cup, mix ¼ cup water with the honey, pepper, and ½ teaspoon salt. Set aside.
In a medium bowl, stir together the flour, turmeric, and 1 teaspoon salt. Add the chicken and toss to coat.
Heat the oil in a 10-inch nonstick skillet over medium-high. Add the chicken and cook until golden brown and fragrant, about 2–3 minutes per side.
Add the asparagus, season lightly with salt, and cook until crisp-tender, about 1–2 minutes.
Pour in the honey mixture and cook, stirring, until the chicken is cooked through and the sauce thickens, 2–3 minutes.
Remove from heat, stir in the vinegar, and season with more salt and pepper to taste. Serve with lime wedges if desired.
