Deep Very Large Telescope/MUSE optical integral field spectroscopy has recently revealed an abundant population of ultra-faint galaxies (M UV ≈ −15; 0.01 L ⋆) at z = 2.9−6.7 due to their strong Ly α emission with no detectable continuum. The implied Ly α equivalent widths can be in excess of 100–200 Å, challenging existing models of normal star formation and indicating extremely young ages, small stellar masses, and a very low amount of metal enrichment. We use JWST/NIRSpec's microshutter array to follow up 45 of these galaxies (11 hr in G235M/F170LP and 7 hr in G395M/F290LP), as well as 45 lower-equivalent width Ly α emitters. Our spectroscopy covers the range 1.7−5.1 micron in order to target strong optical emission lines: H α, [O iii ], H β, and [N II]. Individual measurements as well as stacks reveal line ratios consistent with a metal-poor nature (2%−40% Z ⊙, depending on the calibration). The galaxies with the highest equivalent widths of Ly α, in excess of 90 Å, have lower [N II]/H α (1.9 σ) and [O iii ]/H β (2.2 σ) ratios than those with lower equivalent widths, implying lower gas-phase metallicities at a combined significance of 2.4 σ. This implies a selection based on Ly α equivalent width is an efficient technique for identifying younger, less chemically enriched systems. [ABSTRACT FROM AUTHOR]