Fast radio bursts (FRBs) are millisecond-duration, extragalactic radio flashes of unknown physical origin [1][2][3] . FRB 121102, the only known repeating FRB source [4][5][6] , has been localized to a star-forming region in a dwarf galaxy 7-9 at redshift z = 0.193, and is spatially coincident with a compact, persistent radio source 7,10 . The origin of the bursts, the nature of the persistent source, and the properties of the local environment are still debated. Here we present bursts that show ∼100% linearly polarized emission at a very high and variable Faraday rotation measure in the source frame: RM src = +1.46 × 10 5 rad m −2 and +1.33 × 10 5 rad m −2 at epochs separated by 7 months, in addition to narrow ( 30 µs) temporal structure. The large and variable rotation measure demonstrates that FRB 121102 is in an extreme and dynamic magneto-ionic environment, while the short burst durations argue for a neutron star origin. Such large rotation measures have, until now, only been observed 11,12 in the vicinities of massive black holes (M BH 10 4 M ). Indeed, the properties of the persistent radio source are compatible with those of a low-luminosity, accreting massive black hole 10 . The bursts may thus come from a neutron star in such an environment. However, the observed properties may also be explainable in other models, such as a highly magnetized wind nebula 13 or supernova remnant 14 surrounding a young neutron star.
2Using the 305-m William E. Gordon Telescope at the Arecibo Observatory, we detected 16 bursts from FRB 121102 at radio frequencies from 4.1 − 4.9 GHz (Table 1). The data recorder provided complete polarization parameters with 10.24-µs time resolution. See Methods and Extended Data Figs. 1-6 for observation and analysis details.The 4.5-GHz bursts have typical widths 1 ms, which are narrower than the 2 to 9-ms bursts previously detected at lower frequencies 5,15 . In some cases they show multiple components and structure close to the sampling time of the data. Burst #6 is particularly striking, with a width of 30 µs, which constrains the size of the emitting region to 10 km, modulo geometric and relativistic effects. Evolution in burst morphology with frequency complicates the determination 5 of dispersion measure (DM = d 0 n e (l) dl), but aligning the narrow component in Burst #6 results in DM= 559.7 ± 0.1 pc cm −3 , which is consistent 4,5,15,16 with other bursts detected since 2012, and suggests that any bona fide dispersion measure variations are at the 1% level.After correcting for Faraday rotation, and accounting for ∼2% depolarization from the finite channel widths, the bursts are consistently ∼100% linearly polarized (Fig. 1). The polarization angles PA = PA ∞ + θ (where PA ∞ is a reference angle at infinite frequency, θ = RMλ 2 is the rotation angle of the electric field vector and λ is the observing wavelength) are flat across the observed frequency range and burst envelopes (∆PA 5 • ms −1 ). This could mean that the burst durations reflect the timescale of the emission process and n...