This is the Nurse Chapel episode, the only one that heavily revolves around her. Still, I'm recommending it as viewing for the series itself. Why? Because of that curious subgenre of artificial intelligence that showed up so often but never quite laid the specific groundwork for The Next Generation's Data.
Like McCoy in "The Man Trap," the Chapel story is about a romantic figure from her past. As in the earlier episode, this is not the means to a rekindled romance so much as horror.
By the way, Kirk falls in love this episode, with an android. (In his defense, she's wearing perhaps the prototypical Scantily Clad Babe Suit.)
Chapel's ex has a machine capable of duplicating people in android form. This, naturally, ends up happening to Kirk. After "The Enemy Within," you might have thought you'd seen the last of multiple Kirks running around. Ha! The very last original series movie, Star Trek VI: The Undiscovered Country, of course features this element. For some reason, one Kirk never quite seemed enough.
"Little Girls" has an excellent twist ending that helps distinguish it, one that Next Generation would later duplicate (ha!) in "Inheritance."
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