2001 Chevy Impala security

You have the typical PASSLOCK problem.
Try this relearn procedure:
Turn the key like you're gonna start the car, then let it go back to 'run' position. Wait about ten minutes, and the security light will go off.
Turn key 'off', wait five seconds.
Go thru the same process another two times (three relearns total) and then start your car (after your key has been in the 'off' position for 5 seconds the third time).

This is the GM relearn procedure for your security system. After the third time, your vehicle will learn the passlock Sensor Data Code and/or password on the next ignition switch transition from 'off' to 'start'.

If it fails to fix the problem, you could have a bad passlock sensor.
You'll need to take the car to the dealer and have them check the security system.