In nonorthogonal multiple access (NOMA), the power difference of multiple signals is exploited for multiple access and successive interference cancellation (SIC) is employed at a receiver to mitigate co-channel interference. Thus, NOMA is usually employed for coordinated transmissions and mostly applied to downlink transmissions where a base station (BS) per- forms coordination for downlink transmissions with full channel state information (CSI). In this paper, however, we show that NOMA can also be employed for non-coordinated transmissions such as random access for uplink transmissions. We apply a NOMA scheme to multichannel ALOHA and show that the throughput can be improved. In particular, the resulting scheme is suitable for random access when the number of subchannels is limited since NOMA can effectively increase the number of subchannels without any bandwidth expansion.