Recent experiments have established the glass-forming ability of methylated alkanes. While temperature effects on the glass transition have been extensively studied under ambient pressure, the impact of pressure on molecular mobility at ambient temperature has received less attention. In this work, we use a combination of equilibrium and nonequilibrium molecular simulation methods to determine the viscosity of 2,2,4-tri-methylhexane at 293 K and for pressures ranging from 0.1 MPa to 1 GPa, shedding light on the interplay between structural, thermodynamic and transport properties, leading to the increase in viscosity by several orders of magnitude at high pressure.