Facebook CEO, Mark Zuckerberg has said he won't sell stock in the company for at least 12 months NEW YORK (TIP) : Facebook's stock got some reprieve in after-hours trading Tuesday, September 4 after the company said its CEO, Mark Zuckerberg, won't sell stock in the company for at least the next 12 months, says an AP news report. Investors have been concerned with the expiration of lockup periods that allow insiders to sell stock in Facebook. If a lot of shares flood the market the stock price may fall. Adding to those worries, Peter Thiel, a board member and Facebook's earliest big investor, has shed most of his holdings in the Menlo Park, Calif.-based company. In the Tuesday regulatory filing, Facebook allayed some of those fears.