Is creating a magic weapon that is enhanced with Chill Touch cantrip overpowered for a low level campaign (1-7). I was thinking about giving it a charged based system. Something like 3-5 times per a long rest so it can't be used all the time. This is my first time looking at creating a weapon and would love some constructive input on it. Thanks! 

If it is just a weapon that gives the wielder the ability to cast chill touch as an action, it is fine. If it casts chill touch as part of a weapon attack, that would be pretty strong for tier 1.

Cantrips are already "At-Will", so limiting its activation to 3~5 times per day is unnecessary. The bigger risk is having a Fighter trigger the effect multiple times per round. To play it safe, you could make the effect trigger only on the first successful strike per round of combat.

At low levels, the actual risk is minimal.

What could be fun is making the weapon sentient and having it cast the spell only when it feels like it. Could create RP opportunities.

My eldritch knight has a maul that can cast blade ward. Activating the blade ward is free, and costs 1 charge. The weapon has 6 charges. If I'm ever reduced to 0 hp, the weapon heals me at the expense of 1d4+2 charges. And if there aren't enough charges, I'm teleported in front of Orcus - which is propably bad.

The party's wizard has a ... spider staff thing, which can cast web and spider climb. If the staff runs out of charges, it turns to dust.

I'm guessing the idea is to the wielder activate the Chill Touch power as a free action? Chill Touch is cool, without being wildly OP. Consider having - as you say - limited charges, and maybe a negative effect (burst of AoE necrotic damage maybe?) if it ever runs out of charges. But cool weapon, can do a lot fluff wise with it.

The player is going to expect it to do 2d8 damage at level 5 though, because the spell does. So ... keep that in mind =)

Normally timed magic items go by a 'day' period instead of a rest period. Its just easier. And they have a limit per day like 1, 2 or 3, uses.

You could give instead give it an extra die of the damage type the spell gives.

Magic Items do not normally scale damage by the level of the caster unless it specifically states it.

Memnosyne has the right idea. It should trigger with the first successful attack, but not any successive attacks. I created a weapon for my Conquest Paladin that worships Jergal with this combonation a few years ago. It worked well in game, but did not unbalance anything. It is a unique item that the character carried all the way into tier 3 when the game ended.

Thanks everyone for the responses. Given me some things to think on. Much appreciated!