We analyze the physical layer security of a communication scheme with a multiple antenna legitimate transmitter, employing transmit antenna selection (TAS), and a single antenna legitimate receiver in the presence of a single antenna eavesdropper. We developed closed-form expressions for the analysis of the secrecy outage probability supposing independent and quasi-static Rayleigh fading channels. Our results show that the secrecy outage probability is considerably increased when multiple antennas are available at the legitimate transmitter. Moreover, due to the use of the TAS technique, the eavesdropper is not able to exploit the additional spatial diversity offered by the legitimate transmitter.