Which is the parent chain in Neopentyl chloride? and why? Which is the parent chain in this structure?
and since all have 3 carbons so should any of them be the parent chain, if not ..
then which should be and why? is it a rule in IUPAC naming?

(source: chemspider.com)
A chemist would say that all 3 methyl groups are equivalent (identical by symmetry).  Therefore they all produce the same chain, and that chain is the longest chain in the molecule.  Consequently, since the methyl groups are all the same, it doesn't matter which one you pick.