  A microwave SQUID multiplexer ($\mu$MUX) has been optimized for coupling to
large arrays of superconducting transition-edge sensor (TES) bolometers. We
present the scalable cryogenic multiplexer chip design in a 1820-channel
multiplexer configuration for the 4-8 GHz rf band. The key metrics of yield,
sensitivity, and crosstalk are determined through measurements of 455 readout
channels, which span 4-5 GHz. The median white-noise level is 45
pA/$\sqrt{\textrm{Hz}}$, evaluated at 2 Hz, with a 1/f knee $\leq$ 20 mHz after
common-mode subtraction. The white-noise level decreases the sensitivity of a
TES bolometer optimized for detection of the cosmic microwave background at 150
GHz by only 3%. The measured crosstalk between any channel pair is $\leq$ 0.3%.
