Yes, it is illegal and is an infraction.
Vehicle Code section 5200:
5200. (a) When two license plates are issued by the department for
use upon a vehicle, they shall be attached to the vehicle for which
they were issued, one in the front and the other in the rear.
(b) When only one license plate is issued for use upon a vehicle,
it shall be attached to the rear thereof, unless the license plate is
issued for use upon a truck tractor, in which case the license plate
shall be displayed in accordance with Section 4850.5.
And how to display them is in Vehicle Code section 5201:
5201. License plates shall at all times be securely fastened to the
vehicle for which they are issued so as to prevent the plates from
swinging, shall be mounted in a position so as to be clearly visible,
and shall be maintained in a condition so as to be clearly legible.
The rear license plate shall be mounted not less than 12 inches nor
more than 60 inches from the ground, and the front license plate
shall be mounted not more than 60 inches from the ground . . .
There are some exceptions for different commercial vehicles, but the bottom line is this: If you were issued two plates (as most passenger vehicles are), you’re required to have 2 plates on your car.
It’s a favorite reason for the police to use to pull you over. While it’s typically a “fix-it” ticket and a small fee or fine, it can lead to much bigger problems if they think you’ve been drinking or otherwise want a reason to contact you. Remember – all they need is “reasonable suspicion” of any criminal activity (even a minor traffic equipment violation such as this) to pull you over. Where it goes from there depends on the facts.
If you are pulled over, keep your rights in mind. See this link for more information.