turkish 'sandalye' is most likely borrowed from persian صندلی 'sandali', which is the most common word for chair. it's derived from صندل 'sandal', meaning sandalwood, presumably the most common wood for making chairs at some point.

صندل itself is borrowed from arabic, which had borrowed it from hindi चन्दन / چندن 'chandan'. ('ch' becoming ص in arabic is fairly typical, cf. the persian name for china چین 'chin' becoming صین in arabic). چندن also exists in persian as an archaic word for sandalwood; hindi/urdu also have both 'chandan' and the arabicized 'sandal'.