According to an report at CNET, "Encryption used in Apple's iMessage chat service has stymied attempts by federal drug enforcement agents to eavesdrop on suspects' conversations, an internal government document reveals. An internal Drug Enforcement Administration document seen by CNET discusses a February 2013 criminal investigation and warns that because of the use of encryption, 'it is impossible to intercept iMessages between two Apple devices' even with a court order approved by a federal judge."
The article goes on to talk about ways in which the U.S. government is pressuring companies to leave peepholes for law enforcement in just such apps, and provides some insight into why the proprietary iMessage is (but might not always be) a problem for eavesdroppers, even ones with badges. Adds reader adeelarshad82, "It turns out that encryption is only half of the problem
while the real issue lies in the Communications Assistance for Law Enforcement Act which was passed in 1994.