  We present a theoretical model and experimental characterization of a
microwave kinetic inductance traveling-wave amplifier (KIT), whose noise
performance, measured by a shot-noise tunnel junction (SNTJ), approaches the
quantum limit. Biased with a dc current, the KIT operates in a three-wave
mixing fashion, thereby reducing by several orders of magnitude the power of
the microwave pump tone and associated parasitic heating compared to
conventional four-wave mixing KIT devices. It consists of a 50 Ohms artificial
transmission line whose dispersion allows for a controlled amplification
bandwidth. We measure $16.5^{+1}_{-1.3}$ dB of gain across a 2 GHz bandwidth
with an input 1 dB compression power of -63 dBm, in qualitative agreement with
theory. Using a theoretical framework that accounts for the SNTJ-generated
noise entering both the signal and idler ports of the KIT, we measure the
system-added noise of an amplification chain that integrates the KIT as the
first amplifier. This system-added noise, $3.1\pm0.6$ quanta (equivalent to
$0.66\pm0.15$ K) between 3.5 and 5.5 GHz, is the one that a device replacing
the SNTJ in that chain would see. This KIT is therefore suitable to read large
arrays of microwave kinetic inductance detectors and promising for multiplexed
superconducting qubit readout.
