Indigo

While many associate indigo with India or Egypt, the oldest known indigo-dyed fabric (dated to 6,000 years ago) was discovered in Huaca, Peru. 

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Unlike other dyes that dissolve like sugar in tea, indigo particles just float on top of the water. To get the color onto a fiber, you have to transform it through a specific chemical process that requires a controlled environment which is why it is made in a vat.