Using the concept of "cloning", we report herein a rational approach to grow single-walled carbon nanotubes (SWNTs) with controlled chirality via an open-end growth mechanism. Specifically, by using open-end SWNTs as "seeds/catalysts" (without metal catalysts), "new/duplicate" SWNTs could be grown and cloned from the parent segments via an open-end growth mechanism. Using this strategy, we have measured more than 600 short seed segments and have found that the yield of cloning is relatively low (around 9%). This yield can be greatly improved up to 40% by growing SWNTs on quartz substrate. Atomic force microscopy and micro resonance Raman spectroscopy characterization indicate that the parent nanotube and the duplicate nanotube have the same structure. These findings provide a potential approach for growing SWNTs with controlled chirality, which are important for the application of SWNTs in nanoelectronics.