You would have to pick it up through magical secrets, but this also works with telekinesis as well, is that requires an ability check contesting your opponent's strength. 

When you combine this with the fact that hexblade warlocks get to replace STR and DEX checks/attack rolls with CHA this becomes super busted

Quote from cleb255 >>

When you combine this with the fact that hexblade warlocks get to replace STR and DEX checks/attack rolls with CHA this becomes super busted

 
Hexblade warlock do not replace STR/DEX ability checks with CHA.  Only weapon attack rolls with their pact weapon.

It allows someone with proficiency in any Cha skill to never roll lower than 26 in that skill, and anyone with expertise to break 30 on every roll. The only thing I would change is making it last 8 hours like mind blank or dropping it to 7th level and maybe giving it concentration.

Chalmers: Ah...Aurora Borealis?! At this time of year, at this time of day, in this part of the country, localized entirely within your kitchen!?
Skinner *Casts Glibness*: Yes!
Chalmers: ...May I see it?
Skinner: ...No.

It's Transmutation implying that you are physically transformed in some way to give you the benefits, interesting

Is "the number you roll" the natural number on the die or the number after the modifier?

Natural Number before appropriate pluses or modifiers. Roll a 6, the 6 becomes 15, add pluses.

Quote from tyranttoxicroak >>

8th level? Really? Also shouldn’t this be Emchantment?

 This is really good for casters that use Charisma to Counterspell, especially Lore Bards. An entire hour of being able to flawlessly persuade or lie might be the best RP spell in the game.

Yeah that is so true and really overpowered

Quote from Wulfwithin >>

Quote from tyranttoxicroak >>

8th level? Really? Also shouldn’t this be Emchantment?

 This is really good for casters that use Charisma to Counterspell, especially Lore Bards. An entire hour of being able to flawlessly persuade or lie might be the best RP spell in the game.

Probably worth mentioning that College of Eloquence already grants the ability to never roll less than 10 on Deception and Persuasion checks from 3rd-level, and all Rogues get Reliable Talent at 11th-level to do the same on all checks they are proficient with. Since both can take Expertise in these skills, and Rogues can easily build for high Charisma if they want to, then this means both can become almost impossible to defeat on checks long before glibness becomes available.

That said, it's worth keeping in mind that we're only supposed to roll ability checks when there's a possibility of failure; if your DM wants to run minimum 10/15 as "cannot fail" then they may as well not ask you to roll at all. But the DM is also the one who decides what success actually means; while never being able to get a result of less than 25 or 30 means you can never properly fail a check, that doesn't mean you always get exactly what you wanted without any consequences.

If the DM asks for the roll, then they should still factor in what it was; a low roll on the dice, even if it gets increased to 10 or 15, could still mean that the other person becomes suspicious of you despite having no reason to distrust your words (yet). You might have convinced them to accept your argument, but they can still be uneasy about acting upon it, or reluctant to give you everything you asked for. Maybe they don't need to give you their lifelong unicorn friend as a personal butler on top of the information you went to them for?

So it's only really as overpowered as your DM allows it to be. That said, the ability to power through counterspell/dispel magic or telekinesis checks still makes this a potentially very useful combat spell, especially if you can set it up in advance.

I'm still confused about the Zone of Truth thing. If this spell doesn't counter ZoT, what does it counter? Detect Thoughts and maybe some rarely used magic items or abilities from rare opponents?

Rules As Written (RAW), it does not counter the Zone of Truth. 

Rules As Intended (RAI), some DMs believe it does counter it.  

Mechanically, it gives you the ability to always take a 15 on a CHA ability checks for an hour. 

Narratively, your DM will determine how effective it as at circumventing and evading magic to determine a lie. If you are the DM, just make a call and keep it consistent and reasonable players won't have a melt down.