Since you've only owned the car for a short period of time, I'd say the Chime module is intermittent and was like that when you purchased the vehicle.
Other owners have complained of an intermittent Chime module. The design of the speaker seems to be the problem. Sometimes banging on the dash above the Chime module gets it working again. Replacement seems to be the real cure/solution.
The Tone/Chime module is located behind the DIC (driver information center) which is the display on the right side of the dash that contains/displays the tell tale lamps.
To get to the Chime module requires you remove the top of the dash.
Here's a pic. of the Chime module location.
Here's the schematic of the inputs to the CCM (Central Control module) which controls the Chime module. The CCM monitors the Headlight switch, key in ignition, seat belt switch and if the turn signal is left on for over a mile.
There are 3 Chime tones. Chime 1, Chime 2 and Chime 3. Chime 3 is a combination of Chime 1 and Chime 2.
Chime 1 is for the turn signal left on and also the fasten seat belt.
Chime 2 is for key in ignition and door is open.
Chime 3 is for head light switch if left on and key is out of the ignition.
Here's the schematic of the Chime module
You can place the CCM in diagnostic mode and test the Chime module.
Above the drivers right knee is the Diag. connector and looks like this.
[01|02|03|04|05|06|07|08]
[09|10|11|12|13|14|15|16]
Take a piece of wire and short pin 12 to pin 4.
Turn the ignition ON (don't start the engine).
The speedometer LC display will display any error codes for the PCM, CCM, ABS and Air Bag.
When the display stops.
Press the Trip/ODO button until you see 1.4 in the trip monitor area.
Then press the Eng/Met button until the identifying number for the test to be cycled is shown in the first two digits of the odometer. If it is necessary to go backwards in the list, use the Fuel/Info button.
The status of the output being cycled is shown as a 0 for off and a 1 for on in the last digit of the odometer. Tne output status cycles between On and Off every three seconds.
01 Change Oil indicator
02 Check gauges indicator (engine must be running to see this)
03 Fasten seat belt indicator
04 Security Lamp indicator
05 High bean indicator
06 Chime 1
07 Chime 2
08 LCD Blanking control
09 Rear defogger relay
10 Courtesy lamp relay
11 Low oil indicator
12 Theft deterrent relay
13 Delay accessory bus relay
14 Door ajar indicator
15 Horn relay