In addition to the second harmonic X-mode (X2) electron cyclotron heating (ECH), the TCV ECH system has been completed with three 450 kW gyrotrons operating at the frequency of 118 GHz for third harmonic X-mode (X3) in a top-launch configuration. In the relatively low magnetic field of TCV (1.45 T), the X2 cutoff density is n(e,cutoff)((X2)) = 4 x 10(19) m(-3) and X3 extends the accessible plasma density range up to n(e,cutoff)((X3)) = 11.5 x 10(19) m(-3). The X3 absorption coefficient is lower than that for, X2 by a factor (k(B)T(e))/(m(e)c(2)) and a top-launch injection system has been installed to maximize the beam path along the resonance layer, thus maximizing the optical depth. Theoretical considerations based on a one-dimensional slab geometry model show that the X3 absorption depends mainly on the temperature and the density. It is shown, using a simple two-dimensional model, that in the presence of a suprathermal electron population, the resonance layer width is significantly increased owing to the relativistic shift. The specificity of the top-launch configuration implies that the absorption strongly depends on the propagation direction of the beam. Experimental results are compared with calculations using the linear ray-tracing code TORAY-GA. At the maximum available X3 injected power (1350M), full single-pass absorption is measured, increasing the global electron energy by a factor of 2.5, whereas TORAY-GA predicts only 50% absorption.