Do multiple pieces of chameleon armour stack?

Solution 1:

Yes - legendary item effects stack across multiple pieces of armor.

As discussed here on the Fallout Wikia page for Legendary Armor Effects (my emphasis):

Legendary effects can be added to items by dropping them on the ground and using the console command "attachmod" while having them selected, followed by the mod ID. You can't stack several mods on a single item, but you can stack over multiple pieces (armor). You can also replace a mod with another one via console.

This means that if you have multiple pieces of armor with the same legendary effect, these will stack together.

Solution 2:

Yes... wearing multiple pieces of chameleon armor will stack and give you a greater benefit. Here is a video that shows that:

Solution 3:

I can't comment because I have less than 50 rep so I have to post an answer.

Each piece that has chameleon confers a +20 bonus to stealth. With 5 pieces you get a total of +100 to your ability to remain hidden.

More information:

The Chameleon armor effect (ench_mod_LegendaryArmor_Chameleon) has a magnitude of 20 in the creation kit.

Through testing today I can personally confirm that multiple pieces being equipped in succession can increase your ability to remain hidden and even go from the Danger to Caution state and back as they are equipped and unequipped.