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We present redshift measurements of four faint galaxies around the archetypalultraluminous infrared galaxy Arp 220. These galaxies have significantly higherredshifts ($z \sim$ 0.036 -- 0.091) than that of Arp 220 ($z \simeq 0.018$).Therefore, we conclude that they are background objects not physically relatedto Arp 220. Three of these faint galaxies located to the south of Arp 220 are agroup of galaxies (or the brightest members in a cluster of galaxies) at $z\simeq 0.09$, as suggested by Heckman et al. [1996, ApJ, 457, 616] on the basisof their associated soft X-ray emission.  We also report the serendipitous discovery of three additional galaxies atredshift $z \sim 0.5$, found along one of the slit positions. All threegalaxies exhibit an [O ii] \lambda 3727 emission line. The spectrum of thebrightest galaxy ($m_R \simeq 24.4$) shows other strong emission lines: Mg ii\lambda 2798, H \beta, [O iii] \lambda 4959, and [O iii] \lambda 5007. Theemission-line properties of these galaxies as well as their intrinsically lowluminosities ($M_R \geq -18.4$) indicate that they are star-forming dwarfgalaxies.Comment: 12 pages including 6 tables and 5 figures. Accepted for publication  in A

Redshifts of Galaxies around Arp 220 and Serendipitous Discovery of Three Star-forming Dwarf Galaxies at Redshift [CLC][ITAL]z[/ITAL][/CLC] ∼ 0.5