We analyze the physical layer (PHY) security of a communication scheme consisting of a multiple antenna transmitter with a single radio frequency (RF) chain using transmitter antenna selection (TAS) and a single antenna receiver, in the presence of a sophisticated multiple antenna eavesdropper. We develop closed-form expressions for the analysis of the secrecy outage probability, and we show that the PHY security can be considerably enhanced when multiple antennas are available at the legitimate transmitter. Moreover, a single RF chain multiple antenna transmitter reduces cost, complexity, size and power consumption at the expense of a slight loss in performance with respect to a multiple RF chain transmitter.