  We present SN 2023zaw $-$ a sub-luminous ($\mathrm{M_r} = -16.7$ mag) and
rapidly-evolving supernova ($\mathrm{t_{1/2,r}} = 4.9$ days), with the lowest
nickel mass ($\approx0.002$ $\mathrm{M_\odot}$) measured among all
stripped-envelope supernovae discovered to date. The photospheric spectra are
dominated by broad He I and Ca NIR emission lines with velocities of $\sim10\
000 - 12\ 000$ $\mathrm{km\ s^{-1}}$. The late-time spectra show prominent
narrow He I emission lines at $\sim$1000$\ \mathrm{km\ s^{-1}}$, indicative of
interaction with He-rich circumstellar material. SN 2023zaw is located in the
spiral arm of a star-forming galaxy. We perform radiation-hydrodynamical and
analytical modeling of the lightcurve by fitting with a combination of
shock-cooling emission and nickel decay. The progenitor has a best-fit envelope
mass of $\approx0.2$ $\mathrm{M_\odot}$ and an envelope radius of $\approx50$
$\mathrm{R_\odot}$. The extremely low nickel mass and low ejecta mass
($\approx0.5$ $\mathrm{M_\odot}$) suggest an ultra-stripped SN, which
originates from a mass-losing low mass He-star (ZAMS mass $<$ 10
$\mathrm{M_\odot}$) in a close binary system. This is a channel to form double
neutron star systems, whose merger is detectable with LIGO. SN 2023zaw
underscores the existence of a previously undiscovered population of extremely
low nickel mass ($< 0.005$ $\mathrm{M_\odot}$) stripped-envelope supernovae,
which can be explored with deep and high-cadence transient surveys.
