Sheikh is a homophone of chic. A sheikh is an Arab leader. "Chic" clothing refers to clothing that is stylish. Opulence means a lot of wealth, so the joke is saying the Arab is wealthy and we can tell by his chic clothing. The joke is playing on the word "chic" in "chic clothing" because it sounds like "sheikh". 
The Arab ' s opulence was obvious from his chic clothing . ' '