Hi,
In the Audio/Video section this has been a VERY popular topic for discussion.... The basic problem is the Bezel for the standard radio(s) is not Double Din compatible. They did make a Double Din bezel, also called (or referred) the Navigation Radio Bezel.
These Nav Radio Bezels have seemingly JUMPED in price of late as it has become common knowledge that the company that made these for Chrysler went bankrupt, and thus far, chrysler is not going to engage anybody else to make these items.
Most recent one on ebay went for like $192...others are for sale on ebay buy-it-now at like $240 give or take a few bucks.
This is information I have learned in the past few weeks myself, as I am also a recent owner of my 2007 300 base model.... I am just parroting what others have told me.... KUDO's to them !!