This PDF file includes:

• section S1. Ab initio calculations
  
• section S2. Model parameters
  
• section S3. Tight-binding model
  
• fig. S1. Spatial distribution of the YSR states for a single Fe atom and an Fe dimer on the Re(0001) surface.
  
• fig. S2. The fast Fourier transformation analysis for the magnetic structure of the 40-atom-long Fe chain.
  
• fig. S3. Absence of the in-gap states on the 40-atom-long Fe chain above the superconducting critical temperature of Re.
  
• Legends for movies S1 to S3
  
• References (37–46)

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Other Supplementary Material for this manuscript includes the following:

• movie S1 (.mp4 format). Demonstration of subsequent atom manipulations to construct the close-packed chains of various lengths.
  
• movie S2 (.mp4 format). Spatially resolved 2D spectroscopic maps for two different ends of the 40-atom-long Fe chain below T_C.
  
• movie S3 (.mp4 format). Spatially resolved 2D spectroscopic maps for the 40-atom-long Fe chain above T_C.