Massive multiple-input multiple-output (MIMO) is a key technology in 5G New Radio (NR) to improve spectral efficiency. A major challenge in its realization is the huge amount of real-time computation required. All existing massive MIMO baseband processing solutions use dedicated and specialized hardware like FPGAs, which can efficiently process baseband data but are expensive, inflexible and difficult to program. In this paper, we show that a software-only system called Agora can handle the high computational demand of real-time massive MIMO baseband processing on a single manycore server. To achieve this goal, we identify the rich dimensions of parallelism in massive MIMO baseband processing, and exploit them across multiple CPU cores. We optimize Agora to best use CPU hardware and software features, including SIMD extensions to accelerate computation, cache optimizations to accelerate data movement, and kernel-bypass packet I/O. We evaluate Agora with up to 64 antennas and show that it meets the data rate and latency requirements of 5G NR. CCS CONCEPTS • Networks → Wireless access points, base stations and infrastructure.