The most common reasons a Chrysler 300 makes a ticking noise is low oil level or pressure, the ignition system, or, more uncommonly, an exhaust leak.
Some other sources suggest a few other reasons for a ticking or clicking noise:
Weak battery: A clicking noise from the engine compartment when starting the vehicle could indicate sufficient charge in the battery to activate the solenoid (the source of the clicking) but not enough charge to power the starter.
Poor battery connection: If the battery on your Chrysler 300 is in good health, it may be the connection. If the current flow is interrupted due to a loose electrical connection, a broken wire, or corrosion on the battery terminals, it could lead to a clicking noise.