Superimposed pilots are proposed as an alternative to time-multiplexed pilot and data symbols for mitigating pilot contamination in massive multiple-input multiple-output systems. Provided that the uplink duration is larger than the total number of users in the system, superimposed pilots enable each user to be assigned a unique pilot sequence, thereby allowing for a significant reduction in pilot contamination. Channel estimation performance in the uplink is further improved using an iterative data-aided algorithm. Based on approximate expressions for the uplink signal-to-interference-plus-noise ratio, it is shown that superimposed pilots provide a better performance when compared with methods that use time-multiplexed data and pilots. Numerical simulations are used to validate the approximations and the improved performance of the proposed method.