Trish,

When did you first notice this branch? How has your weather been in you location? One brown branch is not a major concern, the other inner browning is normal for these conifers. Cut off the dead branch and keep an eye on the plant. Have you done any watering of these hinokis ? Recently in my area in PA we have had some hot dry days. These still are new plantings and could benefit from occasional watering ( if you have had similar heat)

We have had wet weather lately. I first noticed this branch this spring. I pruned the dead branch off, should I remove the inner brown stuff?

The branch my have been broken and eventually browned or there is lack of water. Sometimes rain does not make it to the root ball on newly planted shrubs. I define newly planted as within the last 3-4 years. I will occasionally, water each of my newly planted shrubs and trees during the summer and into the fall. Rain is good , however do not assume it is watering deeply. The root balls on plant are sometimes tight and it takes a lot of water to get all the roots wet. This conifer will have some inner browning each year, it is how the old needles ( for lack of better term) die and new form . It does not hurt to clean them out each year. It is up to you. Do you know which hinoki you purchased. some grow slow and small and others get large.

Gracilis. I thought i was buying nana gracilis, so I really bought the wrong kind. They don't have the habit I was looking for but I'm going to give them a few years to decide if they grow on me.

Often conifers don't show damage from dryness (or possibly other problems) for months, so it could have been dryness the year before.

'Nana Gracilis' is a true dwarf, only growing about 5" per year and typically never getting much beyond 6' in height. And a very dense and compact habit, unlike 'Gracilis', which has a much looser and more sculptural growth habit with distinct spacing between the branches. Gracilis is narrow ('gracilis' means slender) but can get tall.......in my climate, 15-25'.