They are aphids. They increase rapidly because much of the time they reproduce by live birth rather than eggs. You'll need to keep spraying with insecticidal soap at intervals. Carbaryl (Sevin) doesn't work reliably for aphids and has even been found to increase them. Another option is to blast them off with as strong a spray of water as you can use without damaging the plant - again you'll likely have to repeat at intervals. For something systemic since you don't mind using "chemicals" you could consider the systemic insecticide Orthene.
