In this paper, a high precision, low ripple 3kV capacitor charging system is investigated, which is designed for the Compact Linear Collider (CLIC). The 240 kW charging system consists of six capacitor charging units operated in boundary conduction mode (BCM). In order to obtain a low current ripple, the charging currents of the units are interleaved. Measurements of the interleaved capacitor charging are provided, which show the stable operation of the interleaving controller. To achieve a high pulse to pulse repeatability of the pulse modulator system, a high charging accuracy of the capacitor bank is mandatory. Thus, a precision analysis of the capacitor charging system is also performed in this paper. With this analysis, the standard deviation of the capacitor bank's voltage is derived for the entire CLIC load operating range, resulting in σvout <23.2 mV, which is below 10 ppm.