\documentclass{amsart}
\begin{document}
$\chi_{A}$
$\chi_{S_{i}}$
\end{document}
I found that the $A$ in $\chi_{A}$ does not look like a subscript; it seems too large. This problem becomes more obvious in the second example, $\chi_{S_{i}}$, which looks like $\chi S_{i}$. How do I fix this?