© 2020. The American Astronomical Society. All rights reserved. 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 1.36 ≤ z ≤ 2.49. We find that the median Lyα and C iii]λλ1907,1909 EWs of our sample are significantly greater than those of z ∼ 2 UV-continuum-selected star-forming galaxies. Measurements from both individual and composite spectra indicate a monotonic, positive correlation between C iii] 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 C iii] 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 C iv λλ1548,1550, He ii λ1640, and O iii]λλ1661,1665 emission in addition to intense Lyα or C iii]. 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.