Bring the wine to a simmer in a large pot over medium-high heat. Add the mussels, cover and reduce the heat to medium low. Cook until the mussels open, about 4 minutes (discard any unopened mussels). Transfer the mussels to a bowl with a slotted spoon. Let cool, then cover and refrigerate until chilled.
Serve the mussels in the shells. Top with the aïoli and chopped chives.