We derive the optimal labor income tax schedule for a life cycle model with deterministic productivity variation and complete asset markets. An individual chooses whether and how much to work at each date. The government must finance a given expenditure and does not have access to lump sum taxation. We develop a solution method that uses the primal approach to solve for the optimal non-linear tax function. The average tax rate determines when an individual will work while the marginal tax rate determines how much she will work. Even in the absence of redistributive concerns, the optimal tax schedule has an increasing average tax rate at low levels of income to encourage labor market participation. The marginal tax rate at the top is strictly positive. Finally, the model is used to assess the effects of changing the current tax schedule to the optimal one. Under the preferred parameters, this delivers a welfare gain equivalent to 0.67 percent of lifetime consumption.