My warning chime goes off at random.

jeep liberty
I suggest you try one of those instant download manuals. My nephew bought one for me when my car broke and we could fix it all by ourselves with the manual costing $10. This website reliable-store.com is very good for this.
?Try it.

When you go to start the vehicle and you turn the key on but not to the start position, all the dash warning lights come on, are they all coming on? IT is very unusual to have a warning chime with no light. I am wondering if a bulb is out in the dash. Or you can go to a store like orielly and have them check the obd codes for free. This will tell you if there is a code stored in the computer showing an error.

check wiring and rotating switch

did you RTM read the operators guide yet,
it tells you why all beeps beep and what lamps flash, (warning) and why. did you?
you turn on, the head lights, (what about 1st click , parking lights"?)
and does the dash cluster, show warnings of any kind?

if a door is ajar the system will think, you are exiting veh. with lights on and tell you, buy beeping ,etc.
but on my jeep it says on the dash DOOR, or on EVICs, (not yours)
the newer car even tells what door IS AJAR.
mine on shows , "DOOR"
the operator guide will say, check all doors for ajar, and get warning clear before driving....etc.

if you lost the guide here it is for free

http://justgivemethedamnmanual.com/jeep/jeep-wrangler-owners-manuals/

click the 05 link
ignore beeps, there are just too many .. i look at the cluster and learn to read it..
my newer jeep 08 can produce 1000s of errors,,,,, possible.
in fact the intent it to beep to tell the driver to look at the cluster
for in depth, causes.
see chapter starting on page 136'

once sound it makes is Check gauges chime. so check them.
and headlamps left on
and door ajar.

page 63
NOTE: If the driver's door is left open, and the headlights
or parking lights are left on, the "High Beam
Indicator Light" will flash and a chime will sound.
Lights-On Reminder
If the headlights or parking lights are on after the ignition
is turned off, a chime will sound when the driver's door

its a crude system, and evolved to complex in 2007.
"DOOR" or RF-door , on mine.
or

NOTE: A tone will chime if the turn signals are left on
for more than 1 mile (2 km).

search manual for
"chime will sound"

sounds like you have a grounding issue possibly a main grounding location. inconsistant grounding of the vehicles control module will cause erratic behaviours. check under the hood for ground locations containing multiple grounds at 1 bolt location.if different "experts" have attempted repair and failed chances are they are all looking in the wrong place.dash{interior of vehicle}..actual cause.{egine compartment or under side of vehicle..ie...ground locations.}good luck and safe motoring:>

Check to see if you have a water level indicator in the top of the radiator . A small plastic fitting with 1 wire from it. IF so it works when there is no water around it and will activate an alarm to warn you of lost water in the cooling system. The problem here is that the radiator cap will allow heated water out to the reservoir but on cooling down insufficient water is drawn back in to keep the top tank completely full. So there is a space that will allow water to miss the unit (cornering-stopping-hills up or down) momenterially and hence the unit chimes intermittently. Check if the top tank is completely full when cool.

check crankshaft sensor.

Sounds like a bad door switch on one of the four doors. The switches have multiple contacts to serve both the dome light and the alarm system. The actual switch button is under a rubber boot with ribbed sides. The switches themselves are under the interior trim behind the doors.

this problem is caused by a tiny micro switch that is attached to the door latch inside the doors, the stick and give this false warning, have replaced dozens of them, it is called the "door ajar" switch oddly enough :)

maybe low on coolant, check water to coolant ratio.