Yes, that's what escape characters are for. To include a character that would otherwise conflict with the string parsing, you need to precede it with a backslash (\). To include an actual backslash, you write a double backslash (\\).
So for your example, the trigger would need to look like the following:
CODE
Display text("Marine: \" Drink A Beer\"
*Drinks*", 4);
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Ha Ha i didn't know that at all (or i forgot). That explains something weird that was happening to me yesterday though.