Anyhow, it actually is pretty easy to do in Illustrator, just not as straight forward.  You need to use the power of the appearance panel (which you can read more about here, here and here) and you won’t technically be putting a gradient on a stroke so much as you’ll be making a fill behave as a stroke and giving that fill a gradient fill.  Yeap.

So we take a basic rectangle shape to start with.

I made an object with a dark green fill and no stroke, placed over a red background shape.

Now, with your object selected, go to the flyout menu of the appearance panel, “Add New Fill”  This will become our stroke.

Right now, all that we have is two overlapping fills, exactly the same.  Select the lower one by clicking on it in the appearance panel.  With the lower fill selected, go up to your Effects menu and go to Effect->Path->Offset Path…  The distance you choose is how far out it will offset your path so choose a distance that is half of what you wanted your stroke width to be. (since your stroke would normally straddle the bounds of your object)  You should be looking at something like this:

All that’s left now is to color the fill that you offset with a gradient.  With that fill still selected in the appearance panel, make it a gradient by choosing a gradient out of the swatches, clicking on the gradient swatch in the gradient panel or by using the gradient tool (if you’re on cs4 or above)

Note that the “stroke” is left blank.  The only thing extending beyond the bounds of our object is our offset fill.  This trick can be applied to any other object, including text.

(on this, I also put an inner glow on the main fill to cut it out of the offset fill)

What’s a counter?

First off, a counter is the opening in a letter; The center of an “o”, the opening in an “e”, those are counters.  This trick will also serve to fill in any spaces in a fill such as those created when a “stroke” in text meets between 2 lines of text.

What’s the trick?

There’s no trick to it – it’s just a simple trick.  I put stroke in quotes up there because this is one of the places we use the Offset Path effect to fake a stroke to add capability not allowed on an ordinary stroke.

Here’s the file, if you want to play along at home.

Apply all of your attributes at the Type layer, leaving your character level with no fill and no stroke.

Add a fill, in this case a red fill.

Add a second fill, and move it below the red fill.  Apricot, in this example.  With that lower fill applied, apply the offset path effect to it by going to Effect -> Path -> Offset Path… I set mine to 3.5 pt, rounded.  This should get you to the upper version of the text – with all the holes in it.

Next – the trick.  Still on that lower fill, after the Offset Path, apply Effect -> Pathfinder -> Divide to it.  Nothing should happen just yet. Now in your appearance panel, click on that effect to edit it.  UN-check “Divide and Outline Will Remove Unpainted Artwork” so that your Pathfinder Options look like these:

Easy-peasy.

I should add that this will also work in any circumstance where Effect -> Offset Path leaves holes that you want to fill, not just with text, though that is where I see the need most often.

Once you’ve read over those 3 posts, download this file and have at it.  You might like to adjust the stroke some to make the “holes” a bit more realistic.

This is live editable text, made awesome, by the appearance panel.