1. Compact stacking of chairs requires a design that allows the chair legs and seating platform to fit neatly within or alongside one another when chairs are placed on top of each other.
2. Option A: The design of \(A\) does not allow for compact stacking because the seat and legs do not align to nest properly.
3. Option B: Similar to \(A\), the design of \(B\) does not allow for stacking, as the seat and legs create obstructions.
4. Option C: The design of \(C\) allows for compact stacking due to its nested structure, where the legs and seat align in a way that minimizes space. Hence, \(C\) is correct.
5. Option D: The design of \(D\) does not allow for stacking as the legs and seating platform obstruct nesting.
Conclusion: The chair that can be compactly stacked is \(C\).