A chip package is described. This chip package includes a stack of semiconductor dies or chips that are offset from each other, thereby defining a terrace with exposed pads. A high-bandwidth ramp component, which is positioned approximately parallel to the terrace, electrically couples to the exposed pads. For example, the ramp component may be electrically coupled to the semiconductor dies using: microsprings, an anisotropic film, and/or solder. Consequently, the electrical contacts may have a conductive, a capacitive or, in general, a complex impedance. Furthermore, the chips and/or the ramp component may be positioned relative to each other using a ball-and-pit alignment technique. By removing the need for costly and area-consuming through-silicon vias (TSVs) in the semiconductor dies, the chip package facilitates chips to be stacked in a manner that provides high bandwidth and low cost.