How do I create tier 3 science packs in Factorio?

Science Pack 3's require a good chunk of research before you hit them. They come from the Battery tech, which itself requires you to research a new resource type: Oil. From there, it just takes Sulfur, and then you can research Battery. You WILL need Plastics, as well, as Plastic Bars are in the resource chain (as part of Advanced Circuits).

Be aware, though, that the amount of resources required for Science Pack 3's are rather heavy, so having the infrastructure in place to make these things is a non-trivial effort.

As of version 0.15.7 0.17.60, the recipe for Science Pack Chemical Science Pack is:

• 1 3 Advanced Circuits
• 1 Electric Mining Drill Sulfur
• 1 2 Engine Units

Batteries (as well as the Filter Inserters) are no longer needed for making them. However, you will still need oil in order to make the Plastic Bars needed for the Advanced Circuit. The Engine Unit also requires Steel Bars, so you will now need to consider a steel bar supply in order to produce these science packs.

As stated in the other answer, you will need to put quite an effort into making these science packs. In my opinion, the current recipe makes it even more difficult to make these science packs.

There is a very handy website I found that shows the Research Tree as of 0.15.8 0.17.79. You can click on the "Chemical Science Pack" technology and it will show you the exact things you need to research and in what order to unlock Science Pack 3 Chemical Science Packs. Currently, it is:

1. Automation and Steel Processing (in either order)
2. Electronics and Logistic Science Pack (in either order)
3. Automation 2 and Engine (in either order)
4. Fluid Handling
5. Oil Processing
6. Plastics
7. Advanced Electronics
8. Chemical Science Pack

Once you research Chemical Science Packs, you will be able to craft Science Pack 3's them.