Legal Question in Landlord & Tenant Law in Kentucky

Speaking as an arachnophobe, yes. Oh my dear Lord have mercy, yes!

Okay, that said, I'm presuming your city has adopted URLTA, the Uniform Residential Landlord-Tenant Act. I certainly think you can craft an argument that under URLTA, your residence is not safe and habitable. However, you need to go about it the right way. You must give your landlord written notice of the spider issue, even if you've complained by phone a thousand times, and give them time (14 days) to make the repairs. I'd argue that it is a construction defect that allows so many hideous creatures to invade your home, and not only are extermination efforts in order, but repairs to keep them from coming back. If the landlord refuses to pay an exterminator, you might just pay an exterminator yourself and tell your landlord you'll deduct the cost from the rent, depending on what that cost is.

Of course, this is all depending upon what your local landlord-tenant law states, and what your lease agreement possibly states about extermination. I would suggest talking to a local attorney, and if you can't afford one, talk to your local Legal Aid office. I happen to know the Legal Aid crew just attended a seminar on Landlord-Tenant Law this week!