We present the first examples of atomic-resolution crystal data for the beta-peptide 12/10-helix from oligomers of cis-2-aminocyclohexane carboxylic acid (cis-ACHC) with alternating chirality. The local conformations of two enantiomeric cis-ACHC dimer units suggested that a chiral beta-peptide may adopt both right-handed and left-handed helical conformations in solution. To probe the conformational behavior of 12/10-helical beta-peptides, the two reference helices with a single handedness were synthesized with a more rigidified cis-ACHC derivative. Comparison with these reference helices at low temperature revealed that a chiral cis-ACHC oligomer with alternating chirality indeed displays 12/10-helical conformations with both handedness that equilibrate rapidly in solution. This is a very rare example of chiral oligomers with helix inversion ability. The 12/10-helical backbone should be a valuable addition to potential scaffolds for applications involving helices with dynamic folding propensity.