GRB 221009A (z=0.151) is one of the closest known long {gamma}-ray bursts (GRBs). Its extreme brightness across all electromagnetic wavelengths provides an unprecedented opportunity to study a member of this still-mysterious class of transients in exquisite detail. We present multiwavelength observations of this extraordinary event, spanning 15 orders of magnitude in photon energy from radio to {gamma}-rays. We find that the data can be partially explained by a forward shock (FS) from a highly collimated relativistic jet interacting with a low-density, wind-like medium. Under this model, the jet's beaming-corrected kinetic energy (E_K_~4x10^50^erg) is typical for the GRB population. The radio and millimeter data provide strong limiting constraints on the FS model, but require the presence of an additional emission component. From equipartition arguments, we find that the radio emission is likely produced by a small amount of mass (<~6x10^-7^M_{sun}_) moving relativistically ({Gamma}>~9) with a large kinetic energy (>~10^49^erg). However, the temporal evolution of this component does not follow prescriptions for synchrotron radiation from a single power-law distribution of electrons (e.g., in a reverse shock or two-component jet), or a thermal- electron population, perhaps suggesting that one of the standard assumptions of afterglow theory is violated. GRB 221009A will likely remain detectable with radio telescopes for years to come, providing a valuable opportunity to track the full lifecycle of a powerful relativistic jet.