Bring to the boil a saucepan of water big enough to hold all the potatoes and corn. Cook the potatoes for 12 mins, adding the corn after 6 mins, until both are tender. Drain well.
Meanwhile, mix the sliced red onion with the lime juice and half the oil in a large salad bowl. Mix the remaining oil with the garlic, paprika and some seasoning in a shallow bowl, then toss in the chicken until thoroughly coated.
Heat a griddle pan, then griddle the chicken for 3 mins on each side until cooked through. Tip the potatoes into the bowl with the onions. Stand a corn cob on one end on a chopping board, then slice down the length, cutting off the kernels in strips. Mix into the potato salad with the coriander and seasoning, then serve alongside the smoky griddled chicken, with lime wedges, if using.