We have constructed a beam-laser lifetime-measuring apparatus and tested it by measuring the well known lifetime of the v = 0 level of the B Z"+ state of Nq+. Our result of 61. 8(5) ns is in excellent agreement with previous high-precision measurements.Employing this technique we performed measurements of the lifetimes of the four lowest vibrational levels of the B Z+ state of Si 0+. The results are (in ns) 69. 5(6), 72. 4(5), 75. 2(5), and 78.0(8) for v = 0, 1, 2, and 3, respectively.PACS number(s): 33.70.Fd