The atomic, binding and electronic structures of very thin Zr chains are studied by the first-principles densityfunctional method. The present calculations reveal that zirconium can form planar chains in zigzag, dimer and ladder structures. The zigzag geometry has two minima. The most stable geometry is the zigzag one with a unit cell rather close to equilateral triangles with four nearest neighbours. The other stable zigzag structure has a wide bond angle and allows for two nearest neighbours. An intermediary structure has the ladder geometry and is formed by two strands. The dimer structure is also found to be more stable than the truly linear chain. All these planar geometries are more favourable energetically than the linear chain. We also show that by going from Zr bulk to a Zr chain, the characters of bonding do not change significantly.