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Gromov asked if the bi-invariant metrics on a compact Lie group are extremal compared to any other metrics. In this note, we prove that the bi-invariant metrics on a compact connected semi-simple Lie group G are extremal (in fact rigid) in the sense of Gromov when compared to the left-invariant metrics. In fact the same result holds for a compact connected homogeneous manifold G/H with G compact connect and semi-simple.doi:10.3842/sigma.2020.068 fatcat:jwjzmwbx5vbjrc4hb4gyk45ra4