We present a new constraint on the Lyman continuum (LyC) escape fraction at z ∼ 1.3. We obtain deep, high sensitivity far-UV imaging with the Advanced Camera for Surveys Solar Blind Channel on the Hubble Space Telescope, targeting 11 star-forming galaxies at 1.2 < z < 1.4. The galaxies are selected from the 3D-HST survey to have high Hα equivalent width (EW) with an EW > 190 Å, low stellar mass (M*< 1010 M⊙), and U-band magnitude of U < 24.2. These criteria identify young, low metallicity star-bursting populations similar to the early star-forming galaxies believed to have reionized the universe. We do not detect any LyC signal (with a signal-tonoise ratio > 3) in the individual galaxies or in the stack in the far-UV images. We place 3σ limits on the relative escape fraction of individual galaxies to be fesc,rel < [0.10-0.22] and a stacked 3σ limit of fesc,rel < 0.07. Measuring various galaxy properties, including stellar mass, dust attenuation, and star formation rate, we show that our measured values fall within the broad range of values covered by the confirmed LyC emitters from the literature. In particular, we compare the distribution of Hα and [O III] EWs of confirmed LyC emitters and nondetections, including the galaxies in this study. Finally, we discuss if a dichotomy seen in the distribution of Hα EWs can perhaps distinguish the LyC emitters from the non-detections.