Few things are more special than spending some quality time snuggling up with parts taken from a murderous AI.
As much as you might want to, you're never going to be able to get your hands on a real Personality Core. Even if they weren't fictional, getting bits of GLaDOS out of the Aperture Science facilities would be practically impossible. If you're willing to settle for huggable, plush facsimiles, however, then Etsy user Katy "Penguinotic" Creider has you covered.
The Personality Core set consists of four plush spheres of slightly different designs. The first is a morality core, the second a curiosity core, the third an intelligence core, and the fourth an anger core. Three of the four cores have a voice box mounted behind their eye, which allows them to say their lines from Portal. Quite appropriately, it's the morality core that remains silent. Each sphere is made of fleece with felt and ribbon accents, and has a circumference of roughly 26".
Creider has actually been making the Personality Core plushies for a while, but she only began selling them in the last few months, and it's only in the last few days that she's started to sell them as a set. You can buy the anger and curiosity cores separately for $45, or you can buy the whole set for $150.