We present the stellar parameters and chemical abundances of 30 elements for five stars located at large radii (3.5–10.7 times the half-light radius) in the Sextans dwarf spheroidal galaxy. We selected these stars using proper motions, radial velocities, and metallicities, and we confirm them as metal-poor members of Sextans with −3.34 ≤ [Fe/H] ≤ −2.64 using high-resolution optical spectra collected with the Magellan Inamori Kyocera Echelle spectrograph. Four of the five stars exhibit normal abundances of C (−0.34 ≤ [C/Fe] ≤ + 0.36), mild enhancement of the α elements Mg, Si, Ca, and Ti ([α/Fe] = +0.12 ± 0.03), and unremarkable abundances of Na, Al, K, Sc, V, Cr, Mn, Co, Ni, and Zn. We identify three chemical signatures previously unknown among stars in Sextans. One star exhibits large overabundances ([X/Fe] > +1.2) of C, N, O, Na, Mg, Si, and K, and large deficiencies of heavy elements ([Sr/Fe] = −2.37 ± 0.25, [Ba/Fe] = −1.45 ± 0.20, [Eu/Fe] < + 0.05), establishing it as a member of the class of carbon-enhanced metal-poor stars with no enhancement of neutron-capture elements. Three stars exhibit moderate enhancements of Eu (+0.17 ≤ [Eu/Fe] ≤ + 0.70), and the abundance ratios among 12 neutron-capture elements are indicative of r-process nucleosynthesis. Another star is highly enhanced in Sr relative to heavier elements ([Sr/Ba] = +1.21 ± 0.25). These chemical signatures can all be attributed to massive, low-metallicity stars or their end states. Our results, the first for stars at large radius in Sextans, demonstrate that these stars were formed in chemically inhomogeneous regions, such as those found in ultra-faint dwarf galaxies.