Does this break normalization? I have an order table, and in the order table I have a contact_id.

Now, each contact is linked to an account. For my order table, should I have both contact_id and account_id?

If I wanted to say, list all orders for account ABC, I could just look through all orders where account_id = "ABC's id"

If I had just the contact_id I would have to go through all the contacts and then pull orders based on each contact_id... this seems kind of like a pain in the neck. 

I don't know if this is really a normalization question, but the easy way seems a little redundant, but I'm not 100% sure. What is the accepted best practices for doing something like this?

Thanks in advance.
There are different levels of normalization.  If your business logic is set up where each contact has an associated account (but more than one contact can be in an account), then there is no reason to put the account ID in the order table because you can get it by going back to the contact table.  In other words, account ID in the contact table is a foreign key.