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The capacity of a multi-time-hopping (MTH) binary pulse position modulation (PPM) ultra-wideband (UWB) system with Rake receivers and Gaussian monocycles supporting variable bit rate (VBR) multiclass services is presented. The analytical framework is formulated for the general case in which different traffic classes have different varying bit rates. The indoor channel model used is based on IEEE 802.15.3a. The analytical work leads to the determination of the system capacity of an MTH binary PPM UWB system with VBR traffic in an indoor multipath environment. Numerical results of the system capacity region are also presented.