Yes, get a harness. As this is a 10 week old you likely will have to use a cat or ferret harness.
These guys are smart. They want to have things their way and they will do all sorts of things to get it. Throwing fits is one of them. As you have to be careful that they don't hurt themselves, but also not reward them for the behavior, you have to become creative.
The biggest thing is to secure him in a manner he can't hurt himself, a harness. Then I'd start by having a string on the harness so it hangs from him. Do this in a small contained area where the sting won't get bound up or stuck on something. Let him get used to a string coming off the harness. Then move forward from there. Change to the leash. Then change to controlling the leash.
Remember he's just a baby and right now you want to focus on fun, positive, and bonding. Establish trust. You may need to give him a containment area for outside (possibly and x-pen) that you can put him for now.
At 10 weeks it may be too soon for you pup.
Also, ask your breeder for input. These are just my suggestions based on my families Chi's. I'm sure your breeder has much more experience then just the Chi's from my history with my family. My old girl LaVie was the worst one on leash training. I was able to work around it until she and, more importantly, I were ready to go through this training. I needed to learn how to get her to trust me and not to reward her for inappropriate behavior.
Good luck!
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tabitha
Kayo, Kahla, and Dante'