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I'm playing a rogue assassin in my current campaign, and I'm about to embark on an infiltration mission where I'll be wearing formal attire. I told the DM I would want to conceal a few lockpicks on my person, but was told (because he was not sure how to rule it) that I would need specifically made attire to accomplish this.

This seemed a little odd to me, and I swear I saw a ruling on this topic somewhere, but haven't been able to find it. Is there an established rule/official ruling out there about hiding small items, especially something like lockpicks?

For something as small as a partial lockpick set I don't even try an ability check for concealing them unless the PC is a joke character with -extremely- low INT or WIS. Hiding things in folds of clothing is second-nature for several classes and for some of the backgrounds.

But if your DM is insisting on a skill check then the closest match is probably (from the Player's Handbook. emphasis mine):

Sleight of Hand

Whenever you attempt an act of legerdemain or manual trickery, such as planting something on someone else or concealing an object on your person, make a Dexterity (Sleight of Hand) check.

The description above has more to do with concealing an item that you just pick pocketed and are still in the area of the target, witnesses and guards but it is the closest match that I know of. It is clearly the rule that would be used if a guard came along while you were trying to work the lock and needed to quickly hide the picks and try to look innocent. Since you would be concealing the items in private and outside of "game time" I would give a large bonus to success on that initial effort to conceal them but just for fun I wouldn't tell you that you had failed that first roll. I would wait and have them come loose at the event, forcing a new slight of hand check to retrieve them from the punch bowl without attracting the attention of guests or servants.