A few weeks ago I started DMing a campaign that involves five divine artifacts that all of the gods' powers are filtered through. I planned on the paragon level quest being collecting these in order to either destroy or protect them. Unfortunately, one of my players rolled a natural 20 on Thievery to steal the chestplate artifact at Level 2 (next encounter will level them up). How should I handle the stats on this item?
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You already let them get the item. Give them the item. Give them the full paragon tier level item. One level 15ish item at +3 (if you are playing DnD 4e) won't significantly destabilize the game. Don't forget to account for the cost of this item in the expected treasure for the party, as well.
As Scott points out in the comments above, you should not be letting players have a 5% chance to totally derail your campaign. This is, however, a great chance to make your campaign feel alive! When the players encounter the next item, there should be enhanced security and word of the daring theft of the last item on the lips of the people around town.
You can make this an "evolving" item, that only reveals its full power over time as the character becomes more attuned to it and puts effort into discovering more of its potential.
That means you can stat it up as a regular 2-to-4th level magic item, and mention that the character can sense greater potential that's locked away. As a bonus, you can "evolve" it into whatever the character would have been awarded as treasure later, making it easier to get their planned items into their hands and simplifying distribution of your treasure parcel's slightly. Just always count each time the chestplate "evoles" as one of the "new" treasures in that adventure's treasure parcel so that you aren't handing out any more than you're intending to.
Rely on the Concordance system to balance/play the artifact
Simple starting advice: stat the item as an appropriate item for the party at its current level (so, a +1 magic armour, possibly with some properties or abilities). Then, modify its stats as its concordance with the party changes.
The artifact's concordance can alter it's properties. Perhaps the armour is unsatisfied with the thief for having stolen it. At Unsatisfied, perhaps the artifact acts as mere +1 magic armor, possibly invoking various other penalties, especially if it makes requests (or demands) of its owners and those requests are denied or failed. If the players act in a manner desirable by the artifact, the concordance can go up and the artifact can share more of its power with its owners. If they anger it, it could penalize them further and, eventually, move on.
Know that in 4th Edition, artifact aren't just powerful items, they're often sentient and powerful beings in their own right, with their own goals and desires. Artifacts seek out owners that can fulfill their wants, and are often only obtained because player characters have done something to make the artifact want to be owned.
Consider, for example, the Standard of Eternal Battle which can only be obtained through conflict. The Standard is otherwise immobile and cannot be picked up, unless the previous owners are defeated in battle by the new owners. That also means the current owners can't willingly get rid of it unless they lose a battle, and the Standard will continually call greater and greater threats tho the party in order to test their mettle.
What does your armour desire? How can the party fulfill its wants? What will the armour do to them if they ignore its demands? How will the armour reward them for pleasing it?
That really depends on your intent.
"The sword chooses its wielder"
Do you want the player to be unable to wield/wear the items? Making the items intelligent can allow the item to refuse to be used by a character that the item does not 'respect' etc. or even risk completely possessing the wearer. Indeed, if a god was meant to wear this equipment, sentience really isn't that far-fetched. And if you've previously outlined that the items don't possess this quality, there's always the next approach...
Known by a variety of names depending on your system (Legacy, Awakened, etc.), the powers at be in the item can be dormant, and need to be awakened over time. This allows your characters to bear them at the time they acquire them without their utility/power falling out of scale as the PCs grow in power.
"____- my only weakness!"
Have a drawback to wearing the items, especially if they're not as powerful as you want them to be when they finally are able to bear them. Penalize a stat point, grant a weakness, etc., but this approach will really only work until the group is strong/rich enough to afford to counteract such penalties. Also be careful to make this god-tier item something that would still be beneficial, in spite of the drawbacks.
Now I'm a target
This type of approach can be used to rend the items from the party, and works especially at lower levels. Obtaining something of great power or story significance can make the group be chased down by those seeking the item or its power. Be careful not to be too cheap if you take this approach ("a bunch of level 18s come and gang bang the party"), and be willing to give the players a fair chance.
You say you've got five of these powerful magical
And they managed to grab one of them way too early?
If so, here's my suggestion:
Stat the chestplate exactly as you would any other similar level-appropriate item. Or maybe a little better — it is a channel of the gods' power, after all. But still, it shouldn't do anything too powerful for the players' level.
That is to say, it shouldn't do anything too powerful alone. But its power should grow non-linearly when combined with the other artifacts.
Specifically, each of the artifacts should have significant additional powers that will only manifest when two of them are brought together. Bring three artifacts together, and they'll each be even more powerful, and four will obviously be much more powerful yet, not to mention the truly godlike level of power that bringing all five of them together should unleash.
Note that you don't need to decide exactly what these extra powers will be yet. That's something that you can defer to the point (hopefully several levels later) when the players manage to collect the next artifact, at which point you can set their combined powers to be something roughly appropriate for their level at the time.
Of course, you should probably make at least some rough plan of what the particular and combined powers of each set of items should be like, even if you don't decide the exact power level in advance. You could even let the players hear rumors of these combined effects, so that they won't be so disappointed by the individual artifacts being less than completely game-breaking awesome.
You'll also want to make sure that, when the players do end up finding the other artifacts, you'll stat them the same way (i.e. weak powers when used alone, increasingly stronger powers when used together), so as to maintain an appearance of consistency.