I have, and the only two things I was successful in growing were potatoes, and mice.
Oh yeah, mice love it under there.

My aunt did straw bale gardening for the first 4 years we were in Swanton. It was moderately successful, but she ended up going with raised beds instead. Your planting options are limited - root vegetables don't work very well. It takes a lot of time, fertilizer and water to prep the bales for planting, and the results depend on weather, placement, etc. We did have some spectacular zuchinni vines, and there were few weeds or pests. Let me know what you decide!

I tried it with strawberries one year--first year was great--second year I had the greatest crop of hay you have ever seen. What a mess

We've all heard of Midas & his golden touch finger...mine's a poo finger for gardening.? I'm am green with gardening envy though??

My sister in law does that and has always had a lot of luck with it. She get twice as much as she did planting in the ground

This guy has been working at it for years.
I ran a few tests two years ago with planting wheat and milo in the fall with mulch.
The test worked out really well. I have pictures, but I didn't keep any numbers.
[onestrawrevolution.net]

I would recommend a good amount of lime, and a lot of compost

That's what I used to do, and it works spectacularly. Better to use straw bales, though, to prevent grass seed getting in your garden soil.

I used to get a few bales, break them open, and spread them over the ground several inches thick, two weeks or so before planting. That gives the straw underneath time to rot into a sort of green slime.

Then all I have to do to plant seeds is poke them into the soft slime, and pull the dry straw on top around the sprouts, as they start to grow. Add more dry straw on top as the plants get taller.

This traps moisture so you don't have to water the garden, and discourages both hungry insects and animals, since they hate to cross the layer of dry straw.

So, it's a "no work" garden. You don't need to water it, or weed it, no pesticides, or fences needed, and when you harvest it, the plants often just keep on producing until the frost.

I have seen it done...they made a hole in the bale and put in potting soil, then planted whatever! Then everything rotted down, from what I remember it works fine! Might do that this year myself!

No, but I want to try it for my potatoes.

I'm not familiar with the concept, but grew up on a farm and see no reason why it wouldn't work. Basically raised bed gardening by the sound of it.
Interesting though...I'll read more of it.

Yes, once in the mountains of L.A., my friend and I planted a huge garden and many plants in straw. Great results btw