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A census of the satellite population around dwarf galaxy primary hosts inenvironments outside the Local Group is essential to understanding $\Lambda$CDMgalaxy formation and evolution on the smallest scales. We present deep opticalHubble Space Telescope imaging of the gas-rich, faint dwarf galaxy Antlia B($M_V = -9.4$) -- a likely satellite of NGC 3109 ($D = 1.3$ Mpc) -- discoveredas part of our ongoing survey of primary host galaxies similar to theMagellanic Clouds. We derive a new tip of the red giant branch (TRGB) distanceof $D = 1.35 \pm 0.06$ Mpc ($m-M = 25.65 \pm 0.10$), consistent with membershipin the nearby NGC 3109 dwarf association. The color-magnitude diagram showsboth a prominent old, metal-poor stellar component and confirms a smallpopulation of young, blue stars with ages $\lesssim 1$ Gyr. We use thecolor-magnitude diagram fitting algorithm MATCH to derive the star formationhistory and find that it is consistent with the typical dwarf irregular ortransitional dwarf galaxy (dTrans) in the Local Group. Antlia B showsrelatively constant stellar mass growth for the first $\sim 10-11$ Gyr andalmost no growth in the last $\sim 2-3$ Gyr. Despite being gas-rich, Antlia Bshows no evidence of active star formation (i.e., no H$\alpha$ emission) andshould therefore be classified as a dTrans dwarf. Both Antlia B and the Antliadwarf (dTrans) are likely satellites of NGC 3109 suggesting that the cessationof ongoing star formation in these galaxies may be environmentally driven.Future work studying the gas kinematics and distribution in Antlia B willexplore this scenario in greater detail. Our work highlights the fact thatdetailed studies of nearby dwarf galaxies in a variety of environments maycontinue to shed light on the processes that drive the star formation historyand evolution of dwarf galaxies more generally.

Hubble Space Telescope Imaging of Antlia B: Star Formation History and a New Tip of the Red Giant Branch Distance