Antiferromagnetic resonance (AFMR) of BaCu2Si2O7 and a microscopic theory of the magnetic anisotropy of spin 1/2 chain compounds with folded CuO3 geometry being in good agreement with the available data are presented. The AFMR studies at 4.2 K show the existence of two gaps (40 and 76 GHz) at zero magnetic field and of two spin re-orientation transitions for H||c. The microscopic origin of the two gaps is shown to be Hunds rule coupling which leads to a residual anisotropy beyond the compensation of the Dzyaloshinskii-Moriya term by the symmetric anisotropy which would be valid without Hunds coupling.
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