TWA 27B (2M1207b) is the first directly imaged planetary-mass (M
p ≈ 5 M
J) companion and was observed at 0.9–5.3 μm with JWST/NIRSpec. To understand the accretion properties of TWA 27B, we search for continuum-subtracted near-infrared helium and hydrogen emission lines and measure their widths and luminosities. We detect the He i triplet at 4.3σ and all Paschen-series lines covered by NIRSpec (Paα, Paβ, Paγ, Paδ) at 4σ–5σ. The three brightest Brackett-series lines (Brα, Brβ, Brγ) as well as Pfγ and Pfδ are tentative detections at 2σ–3σ. We provide upper limits on the other hydrogen lines, including on Hα through Hubble Space Telescope archival data. Three lines can be reliably deconvolved to reveal an intrinsic width Δv
intrsc = (67 ± 9) km s−1, which is 60% of the surface freefall velocity. The line luminosities seem significantly too high to be due to chromospheric activity. Converting line luminosities to an accretion rate yields
M
̇
≈
5
×
10
−
9
M
J
yr
−
1
when using scaling relationships for planetary masses, and
M
̇
≈
0.1
×
10
−
9
M
J
yr
−
1
with extrapolated stellar scalings. Several of these lines represent the first detections at an accretor of such low mass. The weak accretion rate implies that formation is likely over. This analysis shows that JWST can be used to measure low line-emitting mass accretion rates onto planetary-mass objects, motivates deeper searches for the mass reservoir feeding TWA 27B, and hints that other young directly imaged objects might—hitherto unbeknownst—also be accreting.