Archaeological evidence shows that cotton fibres of the genus Gossypium were first used for textile production at Mehrgarh, Pakistan in the Neolithic period ($6^{th}$ millenium BC). Eventually the cotton plant and textiles found their way to Egypt and through there, to Greece. However, the chronological origins of the cultivation and/or use of cotton fibres in textile production in ancient Greece are ambiguous. The main sources of information are ancient written texts and excavated textile finds. Both indicate that the introduction of cotton in Greece can be placed in the mid-first millenium BC. However, it is not clear whether the cultivation of the plant and consequently the production of cotton textiles was established in that period or whether another cotton species was produced and used locally in Greece or whether isolated examples of cotton textiles had been imported in Greece before the cotton plant. A more comprehensive analytical study of surviving textile finds coupled with archaeological research for plant production and cultivation would provide the answer to these questions.