I'm assuming there is no inhibitor chip because Finn disobeys orders.
Why don't they have them anymore and what reason would they have removing them? It seems like a really bad move.
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Jason's answer is basically right, but he's more right that he's guessing.
There is actually a power struggle going on between two competing philosophies of how to get obedient soldiers for the empire. We can source the details from Visual Dictionry as well as film/novelization.
On one hand, we have General Hux, whose father developed techniques for indoctrination while running Imperial academy (source: Visual Dictionary and below quote from novelization).
Ren paused to consider the general’s words. “A simple enough task, or so it would seem. Find one droid. Just how capable are your soldiers, General?”
Hux turned away from the trooper’s holofile. He respected Ren and his abilities, but he was not afraid of him. One did not rise to the rank of general in the forces of the First Order by showing fear.
“I won’t have you questioning my methods.”
“What methods would those be, General? Those that allow a single common trooper to free an important prisoner from confinement, escort him to an operating hangar, and assist him in fighting his way to freedom? What methods teach such expertise? Obviously, at least some of your troops are skilled at high treason. Perhaps Leader Snoke should consider using an army of clones.”
It was with great difficulty that Hux restrained himself. “My men receive exceptional instruction. They are programmed from birth to be loyal to one another, to their officers, and to the Order. The appearance of a single abnormality does not give you the right to question methods that have been refined through long—”
On the other, there are those who oppose the idea and would rather use "more obedient" clones (like Kylo Ren - though there's a chance he's just taking a contrary position because as usual, he's acting like a spoiled teenage Anakin; and not actually taking a principled thought out stand)
The above info also clearly confirms that Finn and the rest of First Order stormtroopers are NOT clones; on top of Jason's excellent points proving that earlier.
The inhibitor chips were added to the Clone Troopers created during the Clone Wars, and they had a very specific purpose: overcome the inconvenient battlefield attachment that would have developed between the Clones and their Jedi Generals when it came time to, y'know, murder them.
But the Stormtroopers aren't clones any more, as you can no doubt tell by the fact that Finn doesn't look like Temuera Morrison, and by Finn at one point revealing that he was taken from his family at a young age:
Finn: I'm a Stormtrooper. Like all of them, I was taken from a family I'll never know, and raised to do one thing.
The Force Awakens (2015)
So he doesn't have one because one was never given to him.
This is pure speculation on my part, but I suspect it's also related to Finn not being a clone. In The Clone Wars CG animated show, we learn that the chips are implanted when the clones are in an early embryonic stage:
AZ-3: My analysis suggests implantation took place at the earliest stage of development, most likely when you [Fives] and Tup were only embryos.
AZ-3: We will start with the earliest stage of development.
AZ-3: I will now try a stage three embryo.
Fives: There it is! Ah. Try another. [the second embryo also has a chip]
AZ-3: Based on this data, I can calculate how many in this tree are altered.
[the console lights up; all the stage three embryos have a chip]
Star Wars The Clone Wars Season 6 Episode 3: "Fugitive"
A later episode suggests that the chip (which is biological) is actually part of the clones' genetic code:
Fives: The evidence is in here [points at his head] It's in all of us. Every clone.
Rex: What is it?
Fives: Organic chips built into our genetic code to make us do whatever someone wants, even kill the Jedi. It's all in here.
Star Wars: The Clone Wars Season 6 Episode 4: "Orders"
This would be difficult for the First Order to manage with a non-Clone Stromtrooper1, so presumably the technology for implanting them at a later stage either doesn't exist, or simply isn't worth the effort.
Instead, the First Order (and possibly the Empire before them) rely on behavioural conditioning; controlling the environment of a growing soldier-to-be is already a great way to get them to obey you in all things, and at one point Captain Phasma remarks that Finn was sent for "reconditioning" after the First Order attack on Jakku:
Phasma: FN-2187 reported to my division, was evaluated ans sent to reconditioning.
Hux: No previous signs of non-conformity?
Phasma: This was his first offense.
The Force Awakens (2015)
1 I suppose it's not beyond the realm of plausibility that the Empire/First Order maintain Stormtrooper breeding facilities, but that's getting a little dark and I'm not going to explore the idea further.