Indoor millimeter-wave (mmWave) environment channels are typically sparsely-scattered and dominated by a strong line-of-sight (LOS) path. Therefore, communication over such channels is in general extremely difficult when the LOS path is not present. However, the recent introduction of reconfigurable intelligent surfaces (RISs), which have the potential to influence the propagation environment in a controlled manner, has the potential to change the previous paradigm. Motivated by this, we study the channel capacity optimization utilizing RISs in indoor mmWave environments where no LOS path is present. More precisely, we propose two optimization schemes that exploit the customizing capabilities of the RIS reflection elements in order to maximize the channel capacity. The first optimization scheme exploits only the adjustability of the RIS reflection elements; for this scheme we derive an approximate expression which explains the connection between the channel capacity gains and the system parameters. The second optimization scheme jointly optimizes the RIS reflection elements and the transmit phase precoder; for this scheme, we propose a low-complexity technique called global co-phasing to determine the phase shift values for use at the RIS. Simulation results show that the optimization of the RIS reflection elements produces a significant channel capacity gain, and that this gain increases with the number of RIS elements.