Reduced-order models (ROMs) leverage modes that arise from time-resolved flow field or mean-flow-linearized Navier-Stokes equations to enable simulation of flow physics at a fraction of the usual computational cost [1]. However, the chosen basis onto which the governing equations are projected affects the accuracy and stability of the ROM [1]. Recently, Cavalieri & Nogueira [2] built a stable ROM of turbulent Couette flow that yielded accurate statistics using a Galerkin projection onto the leading controllability modes from the linearized equations about the laminar solution. In addition, Herrmann et al. [3] recently found that mean-flow-based controllability modes are almost as accurate as proper orthogonal decomposition (POD) modes to represent velocity fluctuations in a turbulent channel flow. In this work, we explore using mean-flow-based balanced modes to build a Petrov-Galerkin ROM of a turbulent channel flow. The resulting model is stable and provides a more accurate reconstruction of turbulence statistics than a ROM built using laminar-flow-based modes. Furthermore, we expect the ROMs built using balanced modes to better preserve the linearization of the underlying system than those using controllability modes.