The density of plated thru holes in a glass fiber based chip carrier is increased by off-setting holes to positions in which fibers from adjacent holes will not connect. Elongated strip zones or regions having a width approximately the diameter of the holes and running along orthogonal columns and rows of holes, parallel to the direction of fibers, define regions of fibers that can possibly cause shorting between holes. Rotating a conventional X-Y grid pattern of equidistant holes so as to position, for example, alternate holes in one direction between the elongated strip zones running in the opposite direction significantly increases the distance between holes along the elongated strip zones running in each direction. The holes are positioned between elongated strip zones with sufficient clearance to compensate for variations in the linear path of fibers.