We present the analysis of seven emph{Chandra} High Energy Transmission Grating Spectrometer and six simultaneous emph{RXTE} Proportional Counter Array observations of the persistent neutron star (NS) low-mass X-ray binary GX 13+1 on its normal and horizontal branches. Across nearly 10 years, GX 13+1 is consistently found to be accreting at $50-70$% Eddington, and all observations exhibit multiple narrow, blueshifted absorption features, the signature of a disk wind, despite the association of normal and horizontal branches with jet activity. A single absorber with standard abundances cannot account for all seven major disk wind features, indicating that multiple absorption zones may be present. Two or three absorbers can produce all of the absorption features at their observed broadened widths and reveal that multiple kinematic components produce the accretion disk wind signature. Assuming the most ionized absorber reflects the physical conditions closest to the NS, we estimate a wind launching radius of $7times10^{10}$ cm, for an electron density of $10^{12}$ cm$^{-3}$. This is consistent with the Compton radius and also with a thermally driven wind. Because of the sources high Eddington fraction, radiation pressure likely facilitates the wind launching.
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