Factory alarm chip, how to bypass the alarm?

If it is the OE alarm system it is built into the Central Timer Module (AKA body control module) and as such there is no real way to bypass it unless you get a module that doesn't have the alarm but that also loses the remote door locks and needs to have an adaption so the vehicle will still run.
The common reason the alarm malfunctions on them is the switch that tells the module to arm and disarm. The problem is that you have what was a somewhat rare option for that year in the trucks and the OE service information doesn't cover it very well and doesn't show if that switch is part of the latch, lock cylinder or lock actuator. On the other vehicles it's part of the door latch itself but the part that comes up for yours shows no switch.
You can try the common reset for them. Use the key in the driver's door, turn it to lock then back to unlock 2 times. On most of them that turns the alarm off until the door is locked again.