Here's the final verdict regarding replacement of the 300L grill running lamp bulb from the 300L technical advisor from the Chrysler 300 Club:
"It is a simple job to do, but the space is a bit tight. You have to reach behind the back of the grille and unscrew the two nuts that hold the running light bezel in place. That's the chrome piece with the red, white & blue circle that surrounds the lens. I think a 3/8" wrench is needed. When the nuts are off, you pull out the bezel and lens from the front and you will see the socket and bulb. Just take out the bulb and put in another. (4 candle power is the right size) Then insert the bezel and lens into place and put the two nuts back on.
The most difficult part is working in the confined space behind the grille."
I hope this clarifies things.