Place the cream cheese in the bowl of an electric mixer fitted with the whisk attachment and whip until it is firm like whipped cream. With the mixer on low speed, slowly add the cream, lemon zest, lemon juice, salt and pepper. Beat on high speed until the mixture is very thick.
Line a 6-inch coeur a la creme mold or 6-inch sieve with a few layers of cheesecloth, allowing the excess to drape over the sides. Pour the cream mixture into the cheesecloth and smooth the top with a rubber spatula. Fold the excess cheesecloth over the top of the cream. Place the mold on a plate or suspend the sieve over a small bowl. Cover with plastic wrap, and refrigerate overnight.
When ready to serve, unmold the creme upside down onto a plate and pour the chutney over the top, allowing it to drip down the sides. Serve chilled with crackers.