To get a Star Chef badge, the experience requires the following qualities:
Hosted by professional chef(s), i.e. trained in high-end restaurants or studied in a well known culinary institute
20+ reviews with an average of 4.7 stars
Wines, plating and venue have to be at a fine dining level
At least 6 dates open in the next 60 days
To summarise, the experience has to be of very high quality!
Please note, community managers review experiences on a constant basis, taking into account requirements for a star chef. Once they get to your experience and your experience matches the criteria, they will add the badge to it!
In situations where you don't have sufficient open dates, the community manger can remove the badge until you schedule more dates.