  Fast Radio Burst FRB 20180916B in its host galaxy SDSS J015800.28+654253.0 at
149 Mpc is by far the closest-known FRB with a robust host galaxy association.
The source also exhibits a 16.35-day period in its bursting. Here we present
optical and infrared imaging as well as integral field spectroscopy
observations of FRB 20180916B with the WFC3 camera on the Hubble Space
Telescope and the MEGARA spectrograph on the 10.4-m Gran Telescopio Canarias.
The 60-90 milliarcsecond (mas) resolution of the Hubble imaging, along with the
previous 2.3-mas localization of FRB 20180916B, allow us to probe its
environment with a 30-60 pc resolution. We constrain any point-like
star-formation or HII region at the location of FRB 20180916B to have an
H$\alpha$ luminosity $L_\mathrm{H\alpha} \lesssim
10^{37}\,\mathrm{erg\,s^{-1}}$ and, correspondingly, constrain the local
star-formation rate to be $\lesssim10^{-4}\,\mathrm{M_\odot\,yr^{-1}}$. The
constraint on H$\alpha$ suggests that possible stellar companions to FRB
20180916B should be of a cooler, less massive spectral type than O6V. FRB
20180916B is 250 pc away (in projected distance) from the brightest pixel of
the nearest young stellar clump, which is $\sim380$\,pc in size (full-width at
half maximum). With the typical projected velocities of pulsars, magnetars, or
neutron stars in binaries (60-750 km s$^{-1}$), FRB 20180916B would need 800
kyr to 7 Myr to traverse the observed distance from its presumed birth site.
This timescale is inconsistent with the active ages of magnetars ($\lesssim10$
kyr). Rather, the inferred age and observed separation are compatible with the
ages of high-mass X-ray binaries and gamma-ray binaries, and their separations
from the nearest OB associations.
