We present an electron spin resonance (ESR) investigation of the acentric Ba(3)NbFe(3)Si(2)O(14), featuring a unique single-domain double-chiral magnetic ground state. Combining simulations of the ESR linewidth anisotropy and the antiferromagnetic-resonance modes allows us to single out the Dzyaloshinsky-Moriya (DM) interaction as the leading magnetic anisotropy term. We demonstrate that the rather minute out-of-plane DM component d(c)=45 mK is responsible for selecting a unique ground state, which endures thermal fluctuations up to astonishingly high temperatures.
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