We consider the unsourced random access problem with multiple receivers and propose a cell-free type solution. In our proposed scheme, active users transmit their signals to the access points (APs) distributed in a geographical area and connected to a central processing unit (CPU). The transmitted signals are composed of a pilot and a polar codeword, where the latter occupies only a small fraction of the data part of the transmission frame. The receiver operations of pilot detection and channel and symbol estimation take place at the APs, while the actual message bits are detected at the CPU by combining the symbol estimates from different APs. The effect of successfully decoded messages is then subtracted at the APs by successive interference cancellation, and the decoding iterations continue with the residual signal. Numerical examples illustrate that the proposed scheme can support up to 1400 users with high energy efficiency, and the distributed structure decreases the error probability by more than two orders of magnitude.