Oil is a very useful substance, but chemistry would certainly still be of immense value even if there was not a drop of oil on Earth. Chemistry is used in some form for most heavy industrial processes from the refining of steel to electroplating.
Of the top 5 chemicals used today all could still be produced. Sulfuric acid production does not use oil and neither does the production of nitrogen or the electrochemical processes that produce caustic soda and bleach. Even propylene and ethylene which are usually produced from oil could be produced from fermentation and oxidation processes without oil.
There are also many other things that can be used to replace oil. The obvious one being coal which would be a good stand in for a number of chemicals normally provided by oil. But even if there was no coal there are many plant based products that could be used as a starting material such as hemp, sunflower and rapeseed oils, timber from which turpentine can be extracted as well as all manner of oils, tars, gums and other chemicals from smoke and condensate from burning organic matter.
Perhaps without oil, gas and coal, the products that currently originate from them would be much more expensive as the alternatives would not be as easily available. So whilst all materials we have today could be produced, their quantity and the financial benefit they represent would be very different. It would be difficult for today’s massive fleets of petrol, diesel, heavy oil and jet fuel guzzling transports to be fueled from plant output.
So it would be a very different world with a very different development trajectory. But chemistry would still be vital.