Yeah, anglicized spellings are all over the place. The dish at our local favorite Thai place was actually spelled ‘pad bi kra pow’. I settled on ‘pad kra pao’ for my post after looking at several spelling versions online. And yes, I think the ‘bai’ or ‘bi’ is basil, so chicken would be ‘pad bai kra pao gai’. Hey, that rhymes!
This is fortuitous. A few weeks ago I had to pick some stuff up from a farmer, and at his gate was a large bush - just by looking at it I could tell it was some fragrant herb, and indeed it smelled heavenly. I asked what it was and if I could take some cuttings. He said it was Thai holy basil and to help myself.
So now I have a couple of holy basil plants thriving in my garden, along with several kinds of chilis, including birds-eye, and a lime tree that produces fragrant leaves. I’m all set!
Basil chicken (or shrimp, or beef, or squid) is one of my go-to dishes at Thai restaurants. I’m a wimp about heat, so they make it mild for me. It looks like it’s a relatively easy dish to make so maybe I’ll give it a go. Surely one of the many Vietnamese markets north of me would carry Thai holy basil.
As an aside, my other favorite Thai dish is a grilled shrimp salad, which is dressed with a lime juice/fish sauce/chili/garlic dressing. It’s crisp, cool, spicy, and refreshing, but not all Thai restaurants make it. If it’s on the menu, I get it every time, together with a basil stir-fry dish.
Now you guys make me want to have Thai for lunch.
My go-to thai salad dressing is simply mashed up chilli, garlic and palm sugar in a mortar and pestle with equal measures of lime juice and fish sauce.
Goes on pretty much anything and I suspect it’s something very much like what you describe.
Cool, I found a nursery only a 1/2 hour drive from me that has a bunch of Thai holy basil plants available; I had been concerned I may have to give up my quest and settle for sweet basil.
Now, once I pick up a few plants, I just have to figure out how to protect them against critters. I’ve had issues in the past with trying to grow basil plants outdoors that were utterly demolished.
I’ve never tried that variety in particular, but the fortunate thing about basil is how easy is to grow from seeds if you do end up having to order them online, and it really doesn’t take long until they are harvestable 
That’s true, I didn’t even think of ordering seeds, and it’s still fairly early in the season if I had to start from seed (I’ve tried overwintering basil plants indoors, and haven’t have very good luck).