Cyclic triureas derived from 1,4,7-triazacyclononane (TACN) were synthesized; X-ray crystallography showed a chiral bowl-like conformation with each urea hydrogen-bonded to its neighbor with uniform directionality, forming a "cyclochiral" closed loop of hydrogen bonds. Variable-temperature 1H NMR, 1H-1H exchange spectroscopy, Eyring analysis, computational modeling, and studies in various solvents revealed that cyclochirality is dynamic (ΔG‡25°C = 63-71 kJ mol-1 in noncoordinating solvents), exchanging between enantiomers by two mechanisms: bowl inversion and directionality reversal, with the former subject to a slightly smaller enantiomerization barrier. The enantiomerization rate substantially increased in the presence of hydrogen-bonding solvents. Population of only one of the two cyclochiral hydrogen-bond directionalities could be induced by annulating one ethylene bridge with a trans-cyclohexane. Alternatively, enantiomerization could be inhibited by annulating one ethylene bridge with a cis-cyclohexane (preventing bowl inversion) and replacing one urea function with a formamide (preventing directionality reversal). Combining these structural modifications resulted in an enantiomerization barrier of ΔG‡25°C = 93 kJ mol-1, furnishing a planar-chiral, atropisomeric bowl-shaped structure whose stereochemical stability arises solely from its hydrogen-bonding network.