Begin by pureeing the fresh blackberries in a blender until smooth. Strain the puree through a fine-mesh sieve to remove the seeds, and set aside the smooth blackberry mixture.
In a large bowl, combine the heavy cream, powdered erythritol, vanilla extract, and unsweetened almond milk. Whisk these ingredients together until the erythritol has dissolved completely.
Slowly sprinkle the xanthan gum over the liquid mixture while continually whisking to prevent clumping. The xanthan gum will help thicken the ice cream and improve its texture.
Fold the strained blackberry puree into the cream mixture until fully incorporated, creating a uniform color.
Gently stir in the sugar-free chocolate chips, distributing them evenly throughout the mixture.
Pour the ice cream mixture into an ice cream maker and churn according to the manufacturer's instructions, usually about 20-30 minutes, or until it reaches a soft-serve consistency.
Transfer the churned ice cream to a freezer-safe container, smoothing the top with a spatula.
Cover the container with a lid or plastic wrap, and freeze for at least 2 hours, or until the ice cream is firm enough to scoop.
Before serving, let the ice cream sit at room temperature for a few minutes to soften for easier scooping.