Using a high-pressure synthesis method, we prepared the layered oxychalcogenide Ba 2 CoO 2 Ag 2 Te 2 (space group: I4/mmm) with alternating stacks of CoO 2 and Ag 2 Te 2 layers, separated by Ba atoms. The CoO 2 plane is greatly extended (Co−O = 2.19 Å on average) due to tensile strain from adjacent Ag 2 Te 2 layers, causing displacement of oxide anions. Layered cobaltates with trans-CoO 4 X 2 (X = chalcogen, halogen) coordination feature large spin−orbit coupling, which is linearly scaled by the tetrahedral factor of d Co−X /d Co−O . However, applying this relation to Ba 2 CoO 2 Ag 2 Te 2 yields a magnetic moment of ∼4 μ B , which is nearly twice the experimentally observed value of 1.87(17) μ B . This result, along with a reduced Neél temperature (T N = 60 K), originates from the off-centered position of otherwise under-bonded oxide anions, which changes the crystal field splitting of Co d orbitals.