In a blender, combine the cilantro, garlic, jalapeño, vinegar and water and puree. Transfer to a bowl and whisk in the mayonnaise. Cover and refrigerate.
In a shallow bowl, lightly beat the eggs. In another shallow bowl, combine the flour, salt and pepper. Spread the potato chips in a third bowl. Lightly coat the chicken with the flour, shaking off any excess, then dip in the beaten eggs. Coat the chicken with the potato chips.
Heat the oil in a large nonstick skillet until shimmering. Add the chicken and cook over moderately high heat until golden and cooked through, about 5 minutes per side. Transfer to plates. Serve at once with the cilantro sauce.