  We present strong constraints on the spacetime variation of the
fine-structure constant $\alpha$ using the Dark Energy Spectroscopic Instrument
(DESI). In this pilot work, we utilize $\sim110,000$ galaxies with strong and
narrow O III $\lambda\lambda$4959,5007 emission lines to measure the relative
variation $\Delta\alpha/\alpha$ in space and time. The O III doublet is
arguably the best choice for this purpose owing to its wide wavelength
separation between the two lines and its strong emission in many galaxies. Our
galaxy sample spans a redshift range of $0<z<0.95$, covering half of all cosmic
time. We divide the sample into subsamples in 10 redshift bins ($\Delta
z=0.1$), and calculate $\Delta\alpha/\alpha$ for the individual subsamples. The
uncertainties of the measured $\Delta\alpha/\alpha$ are roughly between
$2\times10^{-6}$ and $2\times10^{-5}$. We find an apparent $\alpha$ variation
with redshift at a level of $\Delta\alpha/\alpha=(2\sim3)\times10^{-5}$. This
is highly likely to be caused by systematics associated with wavelength
calibration, since such small systematics can be caused by a wavelength
distortion of $0.002-0.003$ \AA, which is beyond the accuracy that the current
DESI data can achieve. We refine the wavelength calibration using sky lines for
a small fraction of the galaxies, but it does not change our main results. We
further probe the spatial variation of $\alpha$ in small redshift ranges, and
do not find obvious, large-scale structures in the spatial distribution of
$\Delta\alpha/\alpha$. As DESI is ongoing, we will include more galaxies, and
by improving the wavelength calibration, we expect to obtain a better
constraint that is comparable to the strongest current constraint.
