Thanks - cutworm was suggested by others as well before I posted here.
Noctuid moth caterpillar by: Moni
AM
The photo is of one of the Noctuid moth caterpillars. As distinctive as it looks, many of the cutworms and armyworm caterpillars look very similar.
This worm looks like both the yellow striped armyworm and the large yellow underwing, as well as like the tobacco cutworm.
Larvae in this family feed on a wide variety of plants such as alfalfa, asparagus, bean, beet, cabbage, clover, corn, cotton, cucumber, grape, grass, jimsonweed, morning glory, onion, pea, peach, peanut, pokeweed, sweet potato, tobacco, tomato, turnip, wheat, watermelon, and wild onion. Now we can add basil. :-)
They live over most of North America.
Here are some photos on bugguide.net -
http://bugguide.net/node/view/9531/bgimage?from=24