This paper intends to study the possibility of submitting to arbitration disputes related to administrative contracts. Hence, private arbitration is analyzed based on Brazilian jurisprudence and doctrine in order to demonstrate the advantages brought by the use of such institution. Additionally, the idea of Public Administration is explored, namely certain principles which guide governmental action and unique aspects of contracts executed by a State. Finally, it shows that arbitration is not only compatible with issues involving alienable rights of a State, but also contributes to put a rapid and efficient end to conflicts - which is definitely a matter of primary public interest. The case of the Guggenheim Museum, commented herein, illustrates the practical relevance of the theme.