I bought a new ignition assembly and it came with 2 blank keys. I'm wondering if instead of having to pay to get them programmed if I could just remove the chip from my original key and put it in the blank key.

 

No, not really. Chip is bonded to the key case, typically destroys the key when you separate the two.

 

What year and model car is this?

For certain years Honda remote cases, this can be done and has been done. For example, some people do this with the 2003-07 Accords.

 

It is a 2006 civic dx.

 

2006 Civic appears similar to 2003-2007 Accords. See this link where the transponder chip is located and extracted from an Accord key fob: https://www.driveaccord.net/threads/new-flip-key.37545/

The ebay link for a Civic shows that the chip (circled) can be swapped: https://www.ebay.com/itm/For-2006-20...0AAOSwKa5c5WYC

 

I did this for my little sisters accord. swapped the chipped portion over to the old key.