Fundamental properties of dipole transmitting antennas formed by carbon nanotubes are investigated. Since carbon nanotubes can be grown to centimeter lengths, and since they can be metallic, the properties of carbon nanotubes as antenna elements are of fundamental interest. In this paper, dipole carbon nanotube antennas are investigated via a classical Hallen's-type integral equation, based on a quantum mechanical conductivity. The input impedance, current profile, and efficiency are presented, and the radiation pattern is discussed, as are possible applications.