Yes, you can have 3 gold chevrons.

By approximately 200BC, two of my Roman stacks were made up almost entirely of 3 gold chevron units of all types (skirmisher, light inf, heavy inf, spearmen, cavalry), with a handful of units with lower experience (as I'd had to replace some depleted units).

Bear in mind though that those two stacks had been fighting almost non-stop in Greece versus the Macedonians and Epirotes for a good 30 years, with a battle every turn or two. So it is not easy at all.

BTW, Principe's with armour and weapon upgrades, and 3 gold chevrons are a sight to behold - during a crap battle with a very small rebel stack with no experience, the killing rate of one of my veteran Principe units head on against...I think it was Samnite spearmen, seemed to be in the realm of 3 or 4 kills per second.

Also, I've had weird retraining issues, where most of the time if I retrain one of my elite stacks in a city, their experience remains the same, but then maybe one time out of every 5 when I retrain the same stack in the same city it seems to drop their experience from an average of gold/silver chevrons to 2 or 3 bronze ones.