This paper solves the optimal asset allocation and consumption pattern of a CRRA investor in case of a single liquid and a single illiquid risky asset, where illiquidity results from restrictions on the trading time of the illiquid asset. The model shows the illiquid asset is less attractive for the short-term investor, whereas the effect of illiquidity is negligible for long-term investors. Moreover, if in certain scenarios the total fraction invested in the illiquid asset becomes sufficiently high and the investor is not able to trade the illiquid asset, the investor reduces her allocation towards the liquid risky asset and the fraction of total wealth to consume. Finally, a positive correlation between the return on the illiquid asset and the probability to be able to trade that asset, leads to an additional reduction in the allocation towards the illiquid asset. This result indicates that the investor faces an increased utility loss if it becomes more difficult to trade the illiquid asset during bad market outcomes.