  A dozen short-period detached binaries are known to host transiting
circumbinary planets. In all circumbinary systems so far, the planetary and
binary orbits are aligned within a couple of degrees. However, the obliquity of
the primary star, which is an important tracer of their formation, evolution,
and tidal history, has only been measured in one circumbinary system until now.
EBLM J0608-59/TOI-1338 is a low-mass eclipsing binary system with a recently
discovered circumbinary planet identified by TESS. Here, we perform
high-resolution spectroscopy during primary eclipse to measure the projected
stellar obliquity of the primary component. The obliquity is low, and thus the
primary star is aligned with the binary and planetary orbits with a projected
spin-orbit angle $\beta = 2.8 \pm 17.1$ deg. The rotation period of $18.1 \pm
1.6$ days implied by our measurement of $v\sin{i_\star}$ suggests that the
primary has not yet pseudo-synchronized with the binary orbit, but is
consistent with gyrochronology and weak tidal interaction with the binary
companion. Our result, combined with the known coplanarity of the binary and
planet orbits, is suggestive of formation from a single disc. Finally, we
considered whether the spectrum of the faint secondary star could affect our
measurements. We show through simulations that the effect is negligible for our
system, but can lead to strong biases in $v\sin{i_\star}$ and $\beta$ for
higher flux ratios. We encourage future studies in eclipse spectroscopy test
the assumption of a dark secondary for flux ratios $\gtrsim 1$ ppt.
