Landau (1937) [1] had an argument that one-dimensional long chains are not stable at finite temperature, and will break into short sections due to thermal fluctuation. However, until recently, fragmentation of one-dimensional chains by formation of thermal vacancies was first discovered in Bagatskii et al. (2014) [6] for the Xenon that physically adsorbed in the grooves of single-walled carbon nanotube bundles. In this work, scanning tunneling microscopy (STM) was first used to observe the influence of thermal fluctuations on the length of one-dimensional chains of the amino acids systems chemically adsorbed on metal surfaces. One-dimensional chains of amino acids formed on noble metal surfaces are spontaneously broken into chain segments with an average length of 46 A at room temperature. Very amazingly, the chain phase shows a unique self-adaptability in that it can always keep the length of chain segments unchanged at a fixed value, which is fulfilled through their flexible orientations, even though there is space limitation. While thermal fluctuation is a stochastic process, breaking of chains does not occur randomly along the chains. Breaking points are equidistantly distributed along the chain with a density (i.e., ratio of breaking points to adsorbates in a chain) of similar to 1/9 at room temperature. After heated to 400 K, the chain segments are shortened to similar to 31 angstrom. And thus, the breaking point density is increased to similar to 1/6. The activation energy for forming a breaking point is similar to 0.04 eV, being within the range of energy for a common hydrogen bond, implying that the amino acid chain is formed by intermolecular hydrogen bonds between adsorbates. The stable spatial distribution of broken points in a chain is resulted from the loss of one-dimensional translational symmetry at the two ends of a chain. This research experimentally first time substantiated both Landau's argument as well as prediction in some recent theoretical simulations. (C) 2018 Elsevier B.V. All rights reserved.