  The Coulomb drag between two spatially separated, 2 \mu m long
lithographically defined quantum wires has been studied experimentally in the
absence of interwire tunneling. The drag resistance R_D shows peaks when the 1D
subband bottoms of the wires are aligned and the Fermi wave vector k_F is
small. R_D decreases exponentially with the interwire separation d. In the
temperature range 0.2K to 1K the drag signal shows the {\it power-law
dependence} R_D ~ T**x with x ranging from -0.61 to -0.77 depending on the
magnitude of k_F. We interpret our experimental results in the framework of the
Tomonaga-Luttinger liquid theory.
