In a small saucepan, combine the 1/4 cup of coconut milk and cocoa powder. Mix hard until it forms a thick paste.
Place paste on medium-low heat, gradually add 1 1/4 cups of milk, about 1/4 cup at a time, stirring constantly until smooth. Cook until small bubble form on the surface, but do not let the mixture boil.
Remove the pan from heat and add the chocolate chips, swirling the pan to keep the chips from resting on the bottom of the pan and burning. Allow the pan to sit off of the stove for about 3 minutes, then stir mixture with a wooden spoon to incorporate the melted chocolate.
Meanwhile, in a blender blend 1/2 cup of coconut milk and xanthan powder until well mixed, about 45 seconds. Mix in the cocoa and vanilla beans until well incorporated.
Transfer the pudding into individual heatproof dishes. Once puddings have cooled slightly, place them in the refrigerator and chill for at least 2 hours.