I'm answering here to flesh some things out, and since I don't have enough reputation to comment (particularly in response to @izak's comment), in case any 4th-edition players are still out there and curious.
By the most conservative interpretation of the rules, the answer is no -- with a workaround available if you are a Gnoll.
The monk unarmed strike is gained via the monk's Unarmed Combatant feature, accessible via classing as a monk or multiclassing Master of the Fist (Dragon 404). The feature is described in Player's Handbook 3, page 63:
When you make a weapon attack such as a melee basic attack, you can
use the monk unarmed strike, which is a weapon in the unarmed weapon
group. This weapon has the off-hand weapon property and a +3
proficiency bonus, and it deals 1d8 damage. You must have a hand free
to use your monk unarmed strike, even if you're kicking, kneeing,
elbowing, or headbutting a target.
Despite being described as "off-hand", and requiring an empty hand to use, your monk unarmed strike is not equivalent to your fist. It is not a great leap to house-rule that if one empty fist is one unarmed strike, then two empty fists count as two melee weapons, but it is up to your DM. One feat's wording to support this conservative ruling is the following Heroic-tier Gnoll feat, "Claw Fighter," from Dragon 367 (emphasis mine):
When you make a weapon attack, you can use your claw, which is a weapon in the light blade weapon group. This weapon has the off-hand weapon property and a +3 proficiency bonus, and it deals 1d6 damage. While you aren't holding anything, you are considered have this weapon in each hand.
The last line specifying having the weapon in each hand is a clarification that the monk unarmed strike does not have, and this would, unequivocally RAW, allow an unarmed Twin Strike -- with the added benefit of Light Blade perks and keeping your multiclass slot free, to boot.
However, even if your DM is conservative in their interpretation, let that not be the end of your unarmed fighting ventures. Several things become clear from the Unarmed Combatant feature description when combined with weapon group descriptions on Player's Handbook 1, page 217: all unarmed strikes count as melee weapons, and monk unarmed strikes specifically can be used for attacks with the weapon keyword (i.e. "weapon attacks").
Thus, even within the strictest interpretation of the rules, it is possible for someone with the Unarmed Combatant feature to have a regular melee weapon in one hand (e.g. a longsword), a monk unarmed strike in the other hand, and perform Twin Strike, Dual Strike, Shocking Twister, or any other such power with the label "Requirement: You must be wielding two melee weapons."
This also applies to the Shock Trooper's level 11 feature (from Martial Power):
When you wield an off-hand weapon, increase the weapon's damage die by one size.
So Master of the Fist multiclass makes your fists +3 1d8 weapons -- as good as a longsword. Notice that fighters with Tempest Technique gain +1 accuracy and +2 damage with offhand weapons, so now your fists would do 1d8+2 damage with a +4 to-hit. Now take Improved Monk Unarmed Strike for 1d10+2 damage, still with +4 to-hit. Pile on Shock Trooper for a 100% rules-legal 1d12+2 off-hand weapon.
Furthermore, with a regular weapon in one hand and an unarmed strike in the other, all two-weapon feats still apply. Two-Weapon Defense, Two-Weapon Opening, etc. Your single fist is, for all intents and purposes, a melee weapon.
In terms of game balance, you're spending a multiclass to get the feature and another feat to boost the die to d10, so there is some opportunity cost. Furthermore, you'll need to use a ki focus to keep up with accuracy, you'll need to take Master at Arms or Versatile Expertise to get the proper +1/tier accuracy boost, and you lose access to weapon-specific feats like Nimble Blade (light blade accuracy) or Heavy Blade Opportunity, but to me it's certainly worth it for the flavor.
Build options for 100% rules-as-written barehanded Gnolls: To combine Tempest Fighter off-hand bonuses with Twin Strike, hybrid and take the Tempest's Hybrid Talent. The Tempest Fighter talent + Shock Trooper feature combine for 1d8+2 claws, and then Light Blade Expertise, Nimble Blade, Swift Blade Style, and weapon enchantments all work -- jagged claws for crits on 19-20, frost claws for Lasting Frost + Wintertouched, etc. No suffering from limited ki focus selection! Furthermore, Tempest Fighters get that juicy +1 accuracy for off-hand weapons, which Gnoll claws qualify for after the Claw Fighter feat. On top of that, you still have a multiclass feat, so you can MC barbarian for Storm of Blades and Hurricane of Blades -- or even better, MC avenger for double rolling attacks and then take Eternal Seeker for grabbing barbarian powers: double rerolls on 7 attacks in one turn with Shocking Twister plus a Hurricane of Blades action point, with 4 more double rerolls available the next turn with Rain of Blows (claws are light blades!) or Cruel Cage of Steel + any ranger minor action attack (Ruffling Sting, Nonchalant Collapse, etc.). Or you could MC rogue for even more minor action attacks, since Gnoll claws, as light blades, are fully compatible with melee rogue powers like Low Slash. Oh, and by the way, Gnolls can charge with at-will powers like Twin Strike (paragon feat, Fierce Charge, Dragon 367) and encounter powers like Shocking Twister and Hurricane of Blades (epic feat, Brutal Charge, Dragon 367).
The sky's the limit. Enjoy your barehanded fighting.