Can you deep fry chicken in a 6.75qt dutch oven?
It depends on the size of the chicken, and how much you want to cook at one time.

Place the bird (or pieces) in your pot and fill the pot to about 3/4 full with water.

Remove the chicken and measure the water...this is how much oil to use. 

If the chicken isn't covered in the water at 3/4 full (this will probably be the case) remove pieces and work backwards till the water and chicken are at a safe level). After replacing the water with oil you will need to work in batches (which is probably what you will need to do, you will probably be well served to do about a 1/2 chicken at a time.).



For what it is worth I recently purchased an infra-red propane 'fryer' that does an excellent job on a whole chicken (or turkey).