Great quote, but it's not by Gibbon. The quotation actually originated in an article by Margaret Thatcher, "The Moral Foundations of Society" (Imprimis, March 1995), which was an edited version of a lecture Thatcher had given at Hillsdale College in November 1994. Here is the actual passage from Thatcher's article:
"[M]ore than they wanted freedom, the Athenians wanted security. Yet they lost everythingsecurity, comfort, and freedom. This was because they wanted not to give to society, but for society to give to them. The freedom they were seeking was freedom from responsibility. It is no wonder, then, that they ceased to be free. In the modern world, we should recall the Athenians' dire fate whenever we confront demands for increased state paternalism."
The quoted passage was written by Thatcher. In characterizing the Athenians in the article she mistakenly cited Sir Edward Gibbon, but she was actually paraphrasing from "Athens' Failure," a chapter of classicist Edith Hamilton's book The Echo of Greece (New York: W. W. Norton & Company, 1967, p.47).