For the Apple Chutney
In a small nonreactive saucepan, combine 1/3 cup sugar, water, ground ginger, chili sauce, jalapeno, and lime juice.  Bring to a boil, stirring to dissolve the sugar.  Boil for 2 minutes. Remove from heat and let cool; strain into a bowl and set aside.

In a medium skillet, melt butter over medium-high heat.  Add apples, onion, and fresh ginger and sauté for 5 minutes, until apple and onion are tender.  In a small bowl whisk remaining ¼ cup sugar, cider vinegar, and apple juice; add to apples along with currants.  Cook, stirring, for 1 minute.

Add lemon zest and reserved chili syrup to apples. Bring to a boil, stirring, for 2 minutes, until mixture is loose and chutneylike.  Remove from heat and let cool to room temperature.  Fold in mint.  Cover and refrigerate until ready to use.

For the Lamb Chops
In a glass dish, stir together honey, red wine vinegar, garlic, oregano, salt, and pepper.  Add lamb, turning to coat.  Marinate lamb, chilled, turning often, for 1 hour.  Bring lamb to room temperature before grilling.

Prepare grill.  When fire is medium-hot (you can hold your hand 5 inches above rack for 3 to 4 seconds), grill lamb on lightly oiled grill rack, turning once, about 4 minutes total for medium-rare.  (The chops should register 120 C to 135 F at the thickest part for rare to medium rare.)

Alternately, lamb can be grilled in batches in a lightly oiled well seasoned ridged grill pan over medium-high heat.  Or you can broil them 3 inches from the flame for 3 minutes per side.

Transfer lamb to plates and spoon apple chutney alongside. Garnish with oregano sprigs and serve immediately.