Could thin layer chromatography separate enantiomers?
The reason is simple: the physical properties of chiral pairs are exactly the same. 

So, for any given compound that is chiral, the melting point, the solubility, the partitioning between liquid and solid phase in a chromatography column etc. are all exactly the same for the pairs of chiral molecules. Simple physical processes can't distinguish the two molecules. The solvents and solid components in chromatography are rarely chiral, so they can't tell the enantiomers apart.

The only things than can are other chiral things. If the solid phase of a chromatography column were chiral (or the solvent, though that is a lot less common) then the column could separate the enantiomers. 

Think of shaking hands. It is natural that a right handed person shakes hand with the right hand of another person but the interaction is radically different if they to shake hands with the other persons left hand. The interaction of chiral things (like hands) depends on chirality. But if you bump fists instead (fists being closer to a sphere which has no handedness) then it matters a lot less which hand your friend uses.