We investigate the performance of wideband massive MIMO base stations that use one-bit ADCs for quantizing the uplink signal. Our main result is to show that the many taps of the frequency-selective channel make linear combiners asymptotically consistent and the quantization noise additive and Gaussian, which simplifies signal processing and enables the straightforward use of OFDM. We also find that single-carrier systems and OFDM systems are affected in the same way by one-bit quantizers in wideband systems because the distribution of the quantization noise becomes the same in both systems as the number of channel taps grows.