Answer
There are 8 valence electrons surrounding each $Cl$.
Work Step by Step
From the diagram, we see that each $Cl$ atom is surrounded by 6 dots (3 nonbonding pairs) and 1 line (1 bonding pair).
That means surrounding each $Cl$ atom are 8 electrons, an octet.
This is reasonable since the purpose of creating a covalent bond with $Si$ is for $Cl$ to have 8 valence electrons so that it can reach the stability of an octet. Each $Cl$ would share 1 electron with 1 electron from $Si$ so that both can use 2 electrons together.
