Steve Hill has stepped down as chief executive of Las Iguanas with immediate effect.
Eren Ali (pictured), the founder of the business, will resume the role of chief executive, until a successor is found.
Bowmark Capital, which owns the business, had been reported to be set to sell the business for up to £100m.
However Las Iguanas said that an potential sale was now unlikely until next year as the company let the eight new sites it plans to open between now and March 2015 time to bed in. It said that as a consequence, Hill had decided to leave to pursue a "portfolio investment career".
The company said research had shown that there is potential over the longer term to grow the brand to at least 120 sites from the current 34 in the UK, and that further "significant opportunities" exist internationally.
Ali said: "Steve has done a great job and we wish him well with his future projects. Having delivered 7% like-for-like growth in the year to March, Las Iguanas is in the best shape it has ever been and I and the rest of the management team are excited by the opportunities that lie ahead for the brand."