Finite index subgroup of Chevalley groups over $\Bbb C$

Question

I'm trying to show that if $G$ is a Chevalley group, then every finite indexed subgroup of $G(\Bbb Z)$ is Zariski dense in $G(\Bbb C)$. ($G(\Bbb Z)$ is the Chevalley group over $\Bbb Z$ and similarly for $G(\Bbb C)$)
But I'm struggling to understand some basic stuff, It seems to me that there can't be finite index subgroup in $G(\Bbb C)$ how can I show that?