Step 1: Define ambidentate ligand.
An ambidentate ligand is a ligand that can coordinate to a central metal atom through two different donor atoms, but only one at a time.
Step 2: Identify ambidentate ligands.
Common ambidentate ligands include $NO_2^-$, $CN^-$, $SCN^-$.
Step 3: Analyze the options.
(A) Diammine silver (I) chloride contains $NH_3$, which is a monodentate ligand.
(B) Sodium hexanitrito-N-cobaltate (III) contains the nitrito ligand $NO_2^-$, which is ambidentate and can coordinate through nitrogen or oxygen.
(C) Tetraaquadichlorochromium (III) chloride contains aqua and chloro ligands, both monodentate.
(D) Barium tetrachlorocuprate (II) contains chloride ligands, which are monodentate.
Step 4: Conclusion.
The complex containing an ambidentate ligand is sodium hexanitrito-N-cobaltate (III).