yes there is. its in your owners manual it involves pushing a bunch of buttons and switches in a certain order.

also if you hit lock on your remote more than once it'll chirp

 

It looks like from the manual, the horn should not be "Chirping" on the first button press. Unless maybe the chirp on the first press is signalling that the alarm is activated.
----------------------------------------------------------------
Remote Lock Feedback
Press the personalization button until REMOTE LOCK
FEEDBACK appears in the display. To select your
personalization for the feedback you will receive when
locking the vehicle with the remote keyless entry
transmitter, press the select button while REMOTE
LOCK FEEDBACK is displayed on the DIC. Pressing
the select button will scroll through the following choices:
LOCK FEEDBACK: BOTH (default): The parking
lamps will flash each time you press the button with the
lock symbol on the remote keyless entry transmitter
and the horn will chirp the second time you press the
lock button.
LOCK FEEDBACK: OFF: There will be no feedback
when locking the vehicle.
LOCK FEEDBACK: HORN: The horn will chirp the
second time you press the button with the lock symbol
on the remote keyless entry transmitter.
LOCK FEEDBACK: LAMPS: The parking lamps will
flash each time you press the button with the lock
symbol on the remote keyless entry transmitter.
Choose one of the four options and press the
personalization button while it is displayed on the DIC to
select it and move on to the next feature.

 

If you go through the dic you should be able to. Also like said above it shouldn't chip with only one press of the fob.

 

but what if I do not have a DIC in my truck?

 

It may or may not be programmable on your truck. Here is a link to the PDF version of your owners manual. If it doesn't tell you how to change it, then you probably can't.
download/chevrolet/silverado/owners_manual/2004_chevrolet_silverado_owners.pdf
Do you have a car alarm on the truck?

 

Yes i do have an alarm.

 

I have a 2006, pretty much same as your 2006. I have my factory alarm set so that when I press the lock button on the keyfob, the parking lights flash, doors lock, and alarm is set, no horn sound. If I press the button repeatedly, it will not chirp the horn either. I did this through the buttons on my steering wheel.

I can write down the exact sequence of what to push later when i go out for lunch, then post back what you should need to do.

Note, if you have an after market alarm, factory settings may not work the same way.

 

If you have an alarm, the chirp could be the alarm arming.

 

I seem to remember a single chirp on first press meant something wasn't right when locking my old GM, and a double chirp was when it locked normally each time (which I did turn off to be silent). A second press would make a single chirp as if to say, "Yeah I heard you." Maybe the single chirp was when I had the door still ajar or something, I forget exactly.