This can be argued either way, depending on how you interpret the words. I'll take a crack at both, and you can pick the one you prefer.
Society necessarily precedes culture. Culture describes the aesthetic habits common to a group of social animals. For culture to develop, those animals must first have developed a social structure within which to share their culture.
Or the counterpoint:
Culture precedes society. Behavior described as culture has been described by behavioral biologists in groups as diverse as birds and whales, whose songs vary group by group between regions, and chimpanzees, who have been observed performing "rain-dances" in stormy weather, and whose vocalizations vary between groups. Neither of these loose social groups - whose leaders and members may change several times in a single season - are complex or organized enough to be considered true societies.