  Strong [OIII]$\lambda\lambda$4959,5007+H$\beta$ 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 Ly$\alpha$ is greatly attenuated by the
intergalactic medium, rest-UV metal emission lines provide an alternative
measure of redshift and also 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 $\sim$ 2 galaxies selected as analogs of
those in the reionization era based on [OIII]$\lambda\lambda$4959,5007 EW or
rest-frame U-B color. Our sample is drawn from the 3D-HST Survey and spans the
redshift range 1.36 $\leqslant$ z $\leqslant$ 2.49. We find that the median
Ly$\alpha$ and CIII]$\lambda\lambda$1907,1909 EWs of our sample are
significantly greater than those of z $\sim$ 2 UV-continuum-selected
star-forming galaxies. Measurements from both individual and composite spectra
indicate a monotonic, positive correlation between CIII] and [OIII], while a
lack of trend is observed between Ly$\alpha$ and [OIII] at [OIII] EW <
1000$\unicode{x212B}$. At higher [OIII] EW, extreme Ly$\alpha$ emission starts
to emerge. Using stacked spectra, we find that Ly$\alpha$ 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
CIV$\lambda\lambda$1548,1550, HeII$\lambda$1640, and
OIII]$\lambda\lambda$1661,1665 emission in addition to intense Ly$\alpha$ 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.
