Combine sugar, water, and jalapeño in a small saucepan. Bring to a boil over high. Reduce heat to medium, and cook, stirring constantly, until sugar dissolves, about 5 minutes. Remove from heat, and cool completely, about 1 hour. Remove jalapeño from syrup, and discard.
Process sugar syrup and 2 cups of the pineapple in a blender on high speed until smooth, about 30 seconds. Finely chop remaining 2 cups of pineapple, and fold into mixture in blender.
Pour mixture evenly into 10 (2-ounce) plastic ice pop molds. Freeze 1 hour. Insert pop sticks, and freeze until solid, about 3 more hours.