Preheat oven to 325 degrees F and place rack in the center of the oven. Butter and lightly flour a 9 x 5 x 3 inch loaf pan. Line the bottom of the pan with a strip of parchment paper.
Melt the chocolate with 1/4 cup of the milk in the microwave, on high, stirring every 15 seconds until smooth. Set aside.
In a separate bowl, whisk the flour with the baking powder and salt.
In a small bowl, whisk the sour cream with the remaining 1/4 cup milk, and the vanilla extract.
With an electric or hand mixer, beat butter and sugar until light and fluffy. Beat in eggs one at a time. On low speed, alternately add the flour mixture and sour cream/milk mixture. Spoon half of the batter into a separate bowl. Add the melted chocolate mixture to one half of the batter and fold in.
With two spoons, place spoonfuls of the two mixtures into the prepared loaf pan alternately (chocolate, white, chocolate, etc.). Run a wooden skewer or knife through the two batters to achieve a marbled effect. Don't over mix.
Bake for about 50 - 55 minutes or until a toothpick inserted in the center comes out clean.
Remove from oven and place on a wire rack to cool for 10 minutes before removing from pan.