How does the Earley Parser store possible parses of an ambiguous sentence?
This is an example of what the graphical chart looks like when there are n tokens in the string:

$\begin{array}{}
[1,1] &amp; [1,2] &amp; [1,3] &amp; \cdots &amp; [1,n] \\
 &amp; [2,2] &amp; [2,3] &amp; \cdots &amp; [2,n] \\
 &amp;  &amp; [3,3] &amp; \cdots &amp; [3,n] \\
 &amp;  &amp;  &amp; \ddots &amp; \vdots \\
 &amp;  &amp;  &amp;  &amp;  [n,n]
\end{array}
$

Because $S$ is the root of the grammar, the two parses of $S$ will be stored in the $[1,n]$ cell of the chart. Here as you can already guess, $[i,j]$ stands for the position indices of the parses, in other word, the span.

In case of $S$, the positions span the whole string. If the positions do not span the whole string, what you have is a set of valid constituent parses in that span.

So the answer to your question is: Possible parses are stored in the same chart, they may be stored in different cells of the chart if their spans are different. If their spans are the same, they are stored in the same cell in the chart.

Btw, I think the first two rules in your grammar do not look right.
Maybe you want 

S -&gt; NP VP and VP -&gt; V NP instead.