Recently, we introduced the idea of chirostrip antennas which are microstrip radiators with chiral materials as substrates and/or superstrates. Owing to the handedness of chiral substrates, novel features are associated with this type of antenna. In this paper, the problem of chirostrip line antennas is analyzed in detail. These antennas consist of an electric line source printed on top of a grounded chiral slab. Both the surface wave and radiation modes of such substrates are obtained and their important features are discussed. Excitation of these surface waves and radiation by the line source are studied and their notable characteristics, such as the power and polarization state of the radiation fields, and the power carried by surface waves, are addressed. It is found that for the two-dimensional chirostrip antenna the chirality can, under certain circumstances, decrease the undesirable surface-wave power and increase the radiated power, thus giving rise to higher radiation resistance and radiation efficiency in these antennas. Such designs would lead to more efficient antennas with wider bandwidth. The physical understanding gained from the analysis of such antennas can help us to introduce novel designs for more complex printed-circuit and conformal antennas utilizing chiral materials. It is concluded that chiral materials can potentially substitute some of the conventional materials commonly used in microwave components and will open new chapters in the design of novel microwave and millimeter-wave devices.