  A fully (pseudo-)spectral solver for direct numerical simulations of
large-scale turbulent channel flows is described. The solver utilizes the
Chebyshev base functions suggested by J. Shen [SIAM J. Sci. Comput., 16, 1,
1995], that lead to stable and robust numerical schemes, even at very large
scale. New and fast algorithms for the direct solution of the linear systems
are devised, and algorithms and matrices for all required scalar products and
transforms are provided. We validate the solver for very high Reynolds numbers.
Specifically, the solver is shown to reproduce the first order statistics of
Hoyas and Jim\'{e}nez [Phys. Fluids, 18(1), 2006], for a channel flow at
$Re_{\tau}=2000$. The solver is available through the open source project
spectralDNS [https://github.com/spectralDNS].
