The short answer really is no, largely depending on your intent.
Technically, you could have your Project(s) on a USB stick instead of the default location - I know you've had difficulties with your project location recently.
However, depends what you mean by 'the chart'.
If you mean what you see on the various Tabs in the Focus Window (Spouses & Children/Parents & Siblings/Ancestors/Descendants) then you can only see them by using the FH software.
The Charts (or more correctly 'Diagrams' that are shown by clicking on the 4 icons on the Toolbar are generated 'on the fly' depending on who is the 'Focus' person.
Other Charts/Diagrams can also be generated, again on the fly or if they are saved.
If you are wanting to give someone your tree, you can either
a) Give them the whole project, but they'd need to purchase the FH software, or
b) Export your tree as a GEDCOM file which can be imported to other software, or even viewed with a Gedcom viewer
c) Export PDF files of your diagram(s)
However, we don't know what your intent is for this question.