YES!!!
Brazil Pepper (Schinus terebinthifolius) is our #1 pest invasive here. I use Garlon 4 (triclopyr 61.8%) Our Conservation unit use it too - they mix it with water and a bit of diesel to ensure good penetration, I'm not too keen on the diesel.
It is best applied on a fresh stump, or you can hack the trunk with a machete and brush it on if you're not removing the tree - aka - mess of impossibly twisted and tangled branches that fight back and poke you in the nose and eyes when you try to cut them.
When you've cut the d*&m thing down, scar up as much of the surface roots as you can find and put the chemical on those too, not just the stump, they have amazing powers of regeneration from distant roots and layered branches.
If you mix a batch of chemical, use it soon as I have found that it tends to lose its potency if left to sit mixed for a week or so. I have a smallish container with a long handled brush attached to the top and just brush the stuff on the cut surfaces.
If you can't get it on the same day you cut it, hack it about with the machete before you put it on. I've found that the gummy sap will prevent the best take up of the herbicide if it is left to sit for a few days.
Over here Garlon is a restricted use herbicide, so you have to be qualified in pesticide application to have it, for those who cant get hold of Garlon the next best is a product called TORDON which I have not used.
Hope this helps - Blasted pepper trees!!!
PS - the species name terebinthifolius refers to the smell of 'turpentine' in the leaves, its related poison ivy so some folks get a reaction to it. The 'pepper' seeds are sometimes used to season fish dishes,not good if you are allergic! It was introduced here in Bermuda as an ornamental because the red berries (peppers) come out at Christmas and are very attractive, its used in a lot of church decorations. Unfortunately the berries are VERY fertile, they germinate in the millions and are disseminated by birds, especially starlings (anothe pest) However the beekeepers like BP as when they are flowering there is not much else out, if we ever got rid of pepper completely (which is unlikely) the honey production would decline quite significantly.