Balsamic Bloody Mary

Ice cubes as needed 

1 cup vodka  

2 cups tomato juice  

1 1/2 Tbs. balsamic vinegar  

1 Tbs. prepared horseradish  

1 tsp. Worcestershire sauce  

4 dashes of Tabasco sauce  

1/4 tsp. celery salt  

Juice of 2 limes  

Freshly ground pepper, to taste 

4 cherry tomatoes  

4 green chilies