Using data taken during the year 2000 with the NA48 detector at the CERN SPS, a search for the CP violating decay K S → 3π 0 has been performed. From a fit to the lifetime distribution of about 4.9 million reconstructed K 0 /K 0 → 3π 0 decays, the CP violating amplitude η 000 = A(K S → 3π 0 )/A(K L → 3π 0 ) has been found to be Re(η 000 ) = −0.002 ± 0.011 ± 0.015 and Im(η 000 ) = −0.003 ± 0.013 ± 0.017. This corresponds to an upper limit on the branching fraction of Br(K S → 3π 0 ) < 7.4 × 10 −7 at 90% confidence level. The result is used to improve knowledge of Re(ǫ) and the CPT violating quantity Im(δ) via the Bell-Steinberger relation.