Before the advent of agriculture, humans fed themselves by hunting and gathering. Hunter-gatherer societies tend to function quite differently from agricultural societies. Arguably, historically, with agriculture came kingdoms, wars, slavery, and overpopulation. In 1987, Jared Diamond wrote an interesting essay on the question.
Could it be different? Could one envision a technologically advanced society¹ that does not do agriculture at all — but still relies on hunting and gathering for feeding the population?
Edit: By agriculture, I mean to actively change and manage land for the intelligent² purpose producing of food or other products (wood, rubber, leather) with a significantly higher yield than would occur naturally. Examples include (but are not limited to) clearing land to grow crops, irrigation, livestock domestication. For the scope of this question I do not consider limited forestry (cutting wood in a naturally growing forest, as opposed to planting forests for wood production) or managed hunting (limiting hunting to prevent species extinction, or hunting competing carnivores such as wolves) to be agriculture. I admit that there are grey zones in this definition (one might speculate on how to categorise in-vitro meat).
¹For the scope of this question, I will arbitrarily define technologically advanced as being able to launch a satellite into orbit.
²Some activities may lead to enhanced food production as a side-effect. For example, water lilies do well in beaver ponds, but beavers probably don't actively plan this, so I do not consider it agriculture for the scope of this question.