  The Galactic Center is host to a population of extraordinary radio filaments,
thin linear structures that trace out magnetic field lines running
perpendicular to the Galactic plane. Using Murriyang, the 64 m Parkes radio
telescope, we conducted a search for pulsars centered on the position of a
compact source in the filament G359.0$-$0.2. We discovered a millisecond pulsar
(MSP), PSR J1744$-$2946, with a period $P = 8.4$ ms, that is bound in a 4.8 hr
circular orbit around a $M_{\rm c} > 0.05\,M_{\odot}$ companion. The pulsar
dispersion measure of $673.7 \pm 0.1$ pc cm$^{-3}$ and Faraday rotation measure
of $3011 \pm 3$ rad m$^{-2}$ are the largest of any known MSP. Its radio pulses
are moderately scattered due to multi-path propagation through the interstellar
medium, with a scattering timescale of $0.87 \pm 0.08$ ms at 2.6 GHz. Using
MeerKAT, we localized the pulsar to a point source embedded in a low-luminosity
radio filament, the "Sunfish", that is unrelated to G359.0$-$0.2. Our discovery
of the first MSP within 1$^{\circ}$ of the Galactic Center hints at a large
population of these objects detectable via high frequency surveys. The
association with a filament points to pulsars as the energy source responsible
for illuminating the Galactic Center radio filaments.
