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We describe the development of a frequency-domain multiplexer (MUX) to read out arrays of superconducting transition-edge sensors (TES). Fabrication of large-format arrays of these sensors is becoming practical; however, reading out each sensor in the array is a major instrumental challenge. Frequency-domain multiplexing can greatly simplify the instrumentation of large arrays by reducing the number of SQUID's (superconducting quantum interference devices) and wires to the low temperature stages. Each sensor is AC biased at a different frequency, ranging from 380 kHz to 1 MHz. Each sensor signal amplitude-modulates its respective AC bias frequency. An LC filter associated with each sensor suppresses Johnson noise from the other sensors. The signals are combined at a current summing node and measured by a single SQUID. The individual signals from each sensor are then lock-in detected by room temperature electronics. Test chips with fully lithographed LC filters for up to 32 channels have been designed and fabricated. The capacitance and inductance values have been measured and are close to the design goals. We discuss the basic principles of frequency-domain multiplexing, the design and testing of the test chips, and the implementation of a practical system.