Evolution of xeno nucleic acid (XNA) world essentially requires template-directed synthesis of XNA polymers. In this study, we demonstrate template-directed synthesis of an acyclic XNA, acyclic L-threoninol nucleic acid (L-aTNA), via chemical ligation mediated by N-cyanoimidazole. The ligation of an L-aTNA fragment on an L-aTNA template is significantly faster and occurs in considerably higher yield than DNA ligation. Both L-aTNA ligation on a DNA template and DNA ligation on an L-aTNA template are also observed. High efficiency ligation of trimer L-aTNA fragments to a template-bound primer is achieved. Furthermore, a pseudo primer extension reaction is demonstrated using a pool of random L-aTNA trimers as substrates. To the best of our knowledge, this is the first example of polymerase-like primer extension of XNA with all four nucleobases, generating phosphodiester bonding without any special modification. This technique paves the way for a genetic system of the L-aTNA world.