It probably depends on the edition. I can tell you that in D&D 3.5, Disintegrate could affect "as much as one 10-foot cube of nonliving matter." You can of course choose to disintegrate less.
To hit with the spell requires a ranged touch attack against the object's AC. Offhand I believe the AC of a single link of chain would be 10 - 5 (Dexterity modifier) -2 (inanimate object penalty) + 8 (fine object) = 11 [http://www.dandwiki.com/wiki/SRD:Breaking_and_Entering.
A Wizard of high enough level to cast the spell would probably have a ranged touch attack modifier of around +5 to +10 at a minimum. If the Wizard takes a full round to line up the shot, he may get a +5 to the roll if the DM rules a ranged touch attack counts as a ranged weapon. So he'd really only fail to hit on a roll of 1, which may lead to hilariously bad results.
Once hit, the object gets a Fortitude Save. A non-magical unattended object always fails its Saving Throw. If the chain is magical, it gets a save with a bonus of 2 + (1/2 the creator's caster level). A failed save deals between 22d6 and 40d6 damage (depending on caster level) and almost certainly destroys the link.
A successful save deals 5d6 damage, although I believe this damage would be reduced by the item's hardness (iron & steel have Hardness 10, mithral is Hardness 15, and adamantine is Hardness 20; all before adding any additional Hardness from spells or the item's nature as a magical object). iron, steel, and mithral have 30 hp/inch of thickness while adamantine has 40 hp/inch of thickness; these numbers are of course before any bonus hp from spells or being a magical object. I'd assume the link of chain to be less than one inch thick, so it'd probably have about 10 to 15 hp (not counting magical enhancement, which generally provides a fixed bonus to hp which doesn't account for the object's thickeness).
Interestingly, the PHB specifically states "A damaged object remains fully functional until the object's hit points are reduced to 0, at which point it is destroyed." So if the link of chain is reduced to one single hp, it will apparently keep functioning just fine according to Rules As Written.
Once the link of chain is successfully disintegrated, the object falls. Here are the damage rules for Falling Objects: http://www.dandwiki.com/wiki/SRD:Falling
The PHB offers no rules for avoiding a falling object, but Heroes of Battle indicates that characters can avoid objects purposefully dropped on them by making a DC 15 Reflex Save (the person dropping the object still has to make an attack roll vs. AC 5 with penalties for range increment and using an improvised weapon; failure means the object lands in a nearby square).
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"Anyone can be a winner if their definition of victory is flexible enough." - The DM of the Rings XXXV
To hit with the spell requires a ranged touch attack against the object's AC. Offhand I believe the AC of a single link of chain would be 10 - 5 (Dexterity modifier) -2 (inanimate object penalty) + 8 (fine object) = 11 [http://www.dandwiki.com/wiki/SRD:Breaking_and_Entering.
A Wizard of high enough level to cast the spell would probably have a ranged touch attack modifier of around +5 to +10 at a minimum. If the Wizard takes a full round to line up the shot, he may get a +5 to the roll if the DM rules a ranged touch attack counts as a ranged weapon. So he'd really only fail to hit on a roll of 1, which may lead to hilariously bad results.
Once hit, the object gets a Fortitude Save. A non-magical unattended object always fails its Saving Throw. If the chain is magical, it gets a save with a bonus of 2 + (1/2 the creator's caster level). A failed save deals between 22d6 and 40d6 damage (depending on caster level) and almost certainly destroys the link.
A successful save deals 5d6 damage, although I believe this damage would be reduced by the item's hardness (iron & steel have Hardness 10, mithral is Hardness 15, and adamantine is Hardness 20; all before adding any additional Hardness from spells or the item's nature as a magical object). iron, steel, and mithral have 30 hp/inch of thickness while adamantine has 40 hp/inch of thickness; these numbers are of course before any bonus hp from spells or being a magical object. I'd assume the link of chain to be less than one inch thick, so it'd probably have about 10 to 15 hp (not counting magical enhancement, which generally provides a fixed bonus to hp which doesn't account for the object's thickeness).
Interestingly, the PHB specifically states "A damaged object remains fully functional until the object's hit points are reduced to 0, at which point it is destroyed." So if the link of chain is reduced to one single hp, it will apparently keep functioning just fine according to Rules As Written.
Once the link of chain is successfully disintegrated, the object falls. Here are the damage rules for Falling Objects: http://www.dandwiki.com/wiki/SRD:Falling
The PHB offers no rules for avoiding a falling object, but Heroes of Battle indicates that characters can avoid objects purposefully dropped on them by making a DC 15 Reflex Save (the person dropping the object still has to make an attack roll vs. AC 5 with penalties for range increment and using an improvised weapon; failure means the object lands in a nearby square).
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"Anyone can be a winner if their definition of victory is flexible enough." - The DM of the Rings XXXV