Preheat the oven to 400 degrees F. Unfold the puff pastry onto a floured piece of parchment paper and roll out into a 9-by-11-inch rectangle. Score 1/2 inch in from the edge, all the way around, using a paring knife. Slide the pastry (on the parchment) onto a baking sheet. Poke the middle all over with a fork, then bake until golden brown, 20 to 25 minutes. Transfer to a rack and let cool completely.
Meanwhile, combine the cream cheese, sour cream, lemon zest, lemon juice, sugar, 1/2 teaspoon salt, and pepper to taste in a large bowl and beat with a mixer on medium speed until smooth; stir in the chives. Spread evenly over the cooled crust. Arrange the tomatoes on top; season with salt and pepper and top with more chives.
You can customize this tart with your favorite toppings.