Invisible (4e Optimized Character Build)
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This is a build that can remain almost constantly invisible at as low a level as 11. Hybrid Rogue/Assassin.
Player's Handbook, Player's Handbook 3, Forgotten Realms Player's Guide, Martial Power, Martial Power 2, Adventurer's Vault, Adventurer's Vault 2, Numerous Dragon Magazine Publications
Game Rule Components
Armor of Dark Deeds, Subtle Rapier, Hand Crossbow
Starting Ability Scores (Before Racial Adjustments): Str 10, Con 11, Dex 17, Int 10, Wis 8, Cha 16
Race (Templates): Drow
Starting Racial Traits: Fey Origin, Lolthtouched, Trance (Drow)
Level 1: Two-Fisted Shooter
Level 2: Pact Initiate
Level 4: Hybrid Talent (Cunning Sneak)
Level 6: Cursed Shadow
Level 8: Drow Fighting Style
Level 10: Versatile Expertise
Level 11: Ruthless Hunter
Level 12: Improved Cunning Sneak
Level 14: Backstabber
Level 16: Spirited Shadows
Level 18: Flash of the Blade
Level 20: Merciless Killer
Level 21: Long Step
Hybrid Talent (Shadow Step)
There are three primary mechanics that make this possible. Cunning sneak allows you to make a stealth check to become invisible if you move at least three squares and have cover. Shadow Step allows you to teleport adjacent to another creature within 5 squares at epic level. Shadow Walk grants concealment if you move 3 or more squares. This allows you to hit a creature, teleport and become invisible, then repeat the process on your next turn.
Armor of Dark deeds grants concealment if you hit a creature granting combat advantage. If you don't want to keep switching targets for the purpose of placing more shrouds on a creature you can use the armor in that manner, then shift 2 squares with Long Step and make the stealth check with Improved Cunning Sneak. The Perfect Slayer epic destiny will make all shrouded creatures grant combat advantage to you and increase your DEX.
Truesight and Tremorsense. The second can be avoided easily with Lightstep slippers. Other than using Sundering Shadow then retreating outside of the creatures vision to use shadow attacks it would be difficult to remain undetected.