The most serious barrier to renouncing your citizenship is that the State Department, which oversees expatriation, is reluctant to allow citizens to go “stateless.” Before allowing expatriation, the department will want you to have obtained citizenship or legal asylum in another country—usually a complicated and expensive process, if it can be done at all. Would-be renunciants must also prove that they do not intend to live in the United States afterward. Furthermore, you cannot renounce inside U.S. borders; the declaration must be made at a consul’s office abroad.
From Harper’s, which has much more, including this:
A more pleasant solution might be found in the Caribbean. Take, for example, the twin-island nation of St. Kitts and Nevis, which Frommer’s guide praises for its “average year-round temperature of 79°F (26°C), low humidity, white-sand beaches, and unspoiled natural beauty.” Citizenship in this paradise can be purchased outright. Prices start at around $125,000, which includes a $25,000 application fee and a minimum purchase of $100,000 in bonds. Processing time, which includes checks for criminal records and HIV, can take up to three months, but with luck you could be renouncing by Inauguration Day.