  Fast radio bursts (FRBs) are bright, coherent, short-duration radio
transients of as-yet unknown extragalactic origin. FRBs exhibit a wide variety
of spectral, temporal and polarimetric properties, which can unveil clues into
their emission physics and propagation effects in the local medium. Here we
present the high-time-resolution (down to 1 $\mu$s) polarimetric properties of
four 1.7-GHz bursts from the repeating FRB 20180916B, which were detected in
voltage data during observations with the European VLBI Network (EVN). We
observe a range of emission timescales spanning three orders of magnitude, with
the shortest component width reaching 3-4 $\mu$s (below which we are limited by
scattering). This is the shortest timescale measured in any FRB, to date. We
demonstrate that all four bursts are highly linearly polarised ($\gtrsim
80\%$), show no evidence for significant circular polarisation ($\lesssim
15\%$), and exhibit a constant polarisation position angle (PPA) during and
between bursts. On short timescales ($\lesssim 100$ $\mu$s), however, there
appear to be subtle (few degree) PPA variations across the burst profiles.
These observational results are most naturally explained in an FRB model where
the emission is magnetospheric in origin, as opposed to models where the
emission originates at larger distances in a relativistic shock.
