Add chocolate chips and 3/4 cup cream to a microwave safe bowl and cook on High for 1 to 2 minutes, stirring every 30 seconds, until smooth. Cool to room temperature. Stir in sugar and vanilla extract. Set aside.
In a bowl, whip remaining 3/4 cup cream until soft peaks form. Beat in chocolate mixture on High speed 1/3 at a time until well mixed. Spoon filling into the pie crust. Refrigerate for at least 8 hours before serving so flavors can develop.