Optoelectronic integrated circuits can support thousands of integrated optical laser diodes and photodetectors bonded to a high-performance CMOS substrate, and can be used in the design of Multi-Terabit optical Local Area Networks. This paper describes the design of an integrated optoelectronic CMOS crossbar switch to interconnect approx. 128 parallel fiber ribbon optical links, each with 12 channels clocked at 2.5 Gigabit/sec, to achieve a Local Area Network (LAN) with an aggregate capacity of 3.84 Terabits/second. A prototype switch core has been designed in 0.18?m CMOS technology. Logic optimization and synthesis was performed using the Synopsis logic optimization tools, and VLSI layout was performed using the Cadence 2002 tools. It is shown that using 0.18?m CMOS technology, a 3.84 Terabit crossbar switch for an optoelectronic LAN occupies approx. 1.78 sq. cm of real estate, and consumes approx. 90 watts of power.