  We report on the diffraction-free propagation of space-time wave packets
(STWPs) -- a class of propagation-invariant pulsed beams -- for $\sim\!1$ km in
an open-air laser range in a low-turbulence scenario. Making use of
$\approx\!100$-fs pulses (bandwidth $\sim\!25$ nm) at a wavelength of
$\approx\!1$ $\mu$m, we construct an STWP with a transverse width of
$\approx\!2$ mm that expands to $\approx\!3$ mm after $\sim\!500$ m, and
another that expands from $\approx\!8$ mm to $\approx\!10$ mm after 1 km. The
propagation of the STWPs is compared to Gaussian wave packets of the same
transverse spatial width and bandwidth. We establish a theoretical model that
accounts for the significant factors limiting the STWP propagation distance and
suggests the path to further extending this distance.
