Analysis of Statement I: $[Fe(ox)_3]^{3-}$ is chiral.

• The complex $[Fe(ox)_3]^{3-}$ involves a central $Fe^{3+}$ ion coordinated to three oxalate ($ox^{2-}$) ligands.
• The oxalate ligand ($ox^{2-}$) is a bidentate ligand, meaning it binds to the metal ion through two donor atoms.
• The complex has the coordination number 6 and adopts an octahedral geometry.
• Complexes of the type $[M(AA)_3]$, where AA is a bidentate ligand like oxalate, are generally chiral. This is because the arrangement of the three bidentate ligands around the central metal atom results in non-superimposable mirror images.
• Specifically, $[Fe(ox)_3]^{3-}$ exists as a pair of enantiomers (dextro and levo rotatory forms).
• Therefore, Statement-I is correct.

Analysis of Statement II: $trans-[Cr(H_2O)_2(ox)_2]^-$ is chiral.

• The complex is $trans-[Cr(H_2O)_2(ox)_2]^-$. It contains a central $Cr^{3+}$ ion, two monodentate water ($H_2O$) ligands, and two bidentate oxalate ($ox^{2-}$) ligands.
• The 'trans' designation indicates that the two $H_2O$ ligands are positioned opposite to each other (180° apart) in the octahedral geometry.
• When the two $H_2O$ ligands occupy trans positions, the two oxalate ligands must coordinate in the remaining four equatorial positions. Each oxalate ligand chelates two adjacent coordination sites.
• In this specific trans configuration, the complex possesses planes of symmetry. One plane can pass through the $Cr$ ion and the two $H_2O$ ligands. Another plane can pass through the $Cr$ ion and contain the four atoms coordinated by the two oxalate ligands.
• The presence of a plane of symmetry makes the molecule achiral.
• Therefore, Statement-II is incorrect.

Conclusion on Statements

Based on the analysis:

• Statement-I is correct.
• Statement-II is incorrect.

This matches the option stating that Statement-I is correct and Statement-II is incorrect.