Try this
var time:Number = 1377564829609;
var date:Date = new Date(time);
The Date class contructor
public function Date(yearOrTimevalue:Object, month:Number, date:Number = 1, hour:Number = 0, minute:Number = 0, second:Number = 0, millisecond:Number = 0)
And the adobe doc said like this
yearOrTimevalue:Object — If other parameters are specified, this number represents
a year (such as 1965); otherwise, it represents a time value.