Strong [O III]λλ4959,5007+Hβ emission appears to be typical in star-forming galaxies at z>6.5. As likely contributors to cosmic reionization, these galaxies and the physical conditions within them are of great interest. At z>6.5, where Lyα is greatly attenuated by the intergalactic medium, rest-UV metal emission lines provide an alternative measure of redshift and constraints on the physical properties of star-forming regions and massive stars. We present the first statistical sample of rest-UV line measurements in z∼2 galaxies selected as analogs of those in the reionization era based on [O III]λλ4959,5007 equivalent width (EW) or rest-frame U − B color. Our sample is drawn from the 3D-HST Survey and spans the redshift range z 1.36 2.49. We find that the median Lyα and CIII]λλ1907,1909 EWs of our sample are significantly greater than those of z∼2 UV-continuum-selected starforming galaxies. Measurements from both individual and composite spectra indicate a monotonic, positive correlation between CIII] and [O III], while a lack of trend is observed between Lyα and [O III] at EW [O III] 1000 Å. At higher EW [O III] , extreme Lyα emission starts to emerge. Using stacked spectra, we find that Lyα and CIII] are significantly enhanced in galaxies with lower metallicity. Two objects in our sample appear comparable to z>6.5 galaxies with exceptionally strong rest-UV metal line emission. These objects have significant CIVλλ1548,1550, HeIIλ1640, and OIII]λλ1661,1665 emission in addition to intense Lyα or CIII]. Detailed characterization of these lower-redshift analogs provides unique insights into the physical conditions in z>6.5 star-forming regions, motivating future observations of reionization-era analogs at lower redshifts. Unified Astronomy Thesaurus concepts: High-redshift galaxies (734); H II regions (694); Emission line galaxies (459)