Yes, starting in 2018. Enacted in December 2017, the Tax Cuts & Jobs Act has a provision that gives employees in privately held companies extra time to pay taxes on the income they recognize at option exercise and RSU vesting. Instead of paying taxes at the exercise of nonqualified options or at the vesting of stock-settled RSUs, employees will be allowed to elect to defer the resulting income, and thus the taxes on that income, for up to five years. This FAQ will soon be expanded and updated to explain the details of the new provision.
For details about the legislation's long development and various rules, see commentaries in the myStockOption blog about its introduction, House approval in 2016, and reintroduction in 2017, when it was called the Empowering Employees Through Stock Ownership Act.