Cut potatoes lengthwise into ¼-inch slices. On a baking sheet, toss potatoes with canola oil. Add smoked paprika and salt, and toss again.
Lay the potatoes slices straight on the grill. Cook until potatoes are tender inside when pierced with a fork, but slightly crisp and golden brown on the outside, turning halfway through cooking, 10 to 12 minutes total. Remove from grill and serve immediately.
If you do not serve immediately, cover potatoes with foil. They will become soft. You can enjoy them this way or re-crisp on the grill immediately before serving.