You are making cookies and add N chips to dough randomly, and split it into 100 equal cookies, again at random. How many chips should go into dough? Question: You are making chocolate chip cookies. You add N chips randomly to the dough and you randomly split the dough into 100 equal cookies. How many chips should go into the dough to give a probability of at least 90% that every cookie has at least one chip?

I tried to attempt to solve this using IID random variables. I am not sure how to set the problem up. I know that there should at least be 100 chocolate chips or else the cookies will not meet the "at least 1 chip per cookie" requirement and that there is 10% chance that the cookies do not have a chip.
There seem to be several interpretations of what you are looking for.
I have revised my answer to make it clear what I am answering, and appended a comment for a different interpretation.

I'd suggest an approximate Poisson model.  If there are $N$ chips in the dough,
then the number of chips in a random cookie is $X \sim Pois(\lambda = N/100).$
You want a 90% probability that a random cookie has at least
one chip, then solve for $N$ in $$1 - P\{X = 0\} = 1 - e^{-N/100} = .90.$$

Addendum: If you want a 90% chance that every one of the 100 cookies has
at least one chip, then that's another problem, to which the
Coupon Collection approach suggested in another Answer is a specific idea that may be
appropriate. There are Comments with
strong opinions about approaches, but no specific suggestions yet.
If there is a requirement that the chocolate chips are evenly (or "equally") distributed, then you need at least 100 chips in order for there to be a non-zero probability of having at least 1 chip in every cookie. But then there will be a 100% probability that every cookie will have a chip in it because the chips are evenly distributed, so $N=100$.

On the other hand, if you believe that the chips were "randomly" distributed, you would need to know the maximum amount of chips which could fit into 1 cookie, and assume that every cookie is the same size. You would also need a function to describe the "randomness" - i.e. if some cookies will get more chips than others and by how much.