We present the results of a low-resolution spectral abundance study of 25 stars in the Boötes I dwarf spheroidal ( dSph ) galaxy . The data were obtained with the LRIS instrument at Keck Observatory , and allow us to measure [ Fe/H ] , [ C/Fe ] , and [ \alpha /Fe ] for each star . We find both a large spread in metallicity ( 2.1 dex in [ Fe/H ] ) as well as the low average metallicity in this system , \langle [ Fe/H ] \rangle = -2.59 , matching previous estimates . This sample includes a newly discovered extremely metal-poor star , with [ Fe/H ] = -3.8 , that is one of the most metal-poor stars yet found in a dSph . We compare the metallicity distribution function of Boötes I to analytic chemical evolution models . While the metallicity distribution function of Boötes I is best fit by an Extra Gas chemical evolution model , leaky-box models also provide reasonable fits . We also find that the [ \alpha /Fe ] distribution and the carbon-enhanced metal-poor fraction of our sample ( 12 % ) are reasonable matches to Galactic halo star samples in the same metallicity range , indicating that at these low metallicities , systems like the Boötes I ultra-faint dSph could have been contributors to the Galactic halo .