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Given the context I think that this sentence means "it's probably an
unintentional action".

But I am unsure of what meaning/nuance the うち adds here. I am used to seeing
うち meaning "while" and that's what I'm seeing on various internet sources. But
I don't see how a "while" fits into this sentence.
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word-choice words
Meaning of うち in "無意識のうちの行動なのだろう"
In that context, 「うち」 refers to the _**situation**_ in which an action is
performed or an event takes place.

"While" would not always work as a translation. In fact, I feel that you are
thinking of another usage of 「うち」 which describes temporal relationships.

> 「Intangible Noun + の + うち + **の** + Noun」
>
> = "(Noun) taking place in the situation described by (Intangible Noun)"

「[無意識]{むいしき}の **うち** の[行動]{こうどう}」 = "an action performed in (the realm of)
unconsciousness"

> 「Intangible Noun + の + うち + **に** + Verb Phrase」

「オリンピックは[成功]{せいこう}の **うち** に[終]{お}わった。」 = "The Olympics ended in success"
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「無意識のうち」is an expression, actually.

You can find out more of the specific meanings in
[http://thesaurus.weblio.jp/content/無意識のうちに](http://thesaurus.weblio.jp/content/%E7%84%A1%E6%84%8F%E8%AD%98%E3%81%AE%E3%81%86%E3%81%A1%E3%81%AB)

It is still the same "while" meaning, but in English it is not translated that
way, since the while is implied. "It was probably done while not being aware"
would be the literal translation.
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Just like ShikiGami said, it also means "while" here. You can translate it to
something like... "It must be/must have been probably a behavior taken "while"
being in one's unconscious mind." Hope this helps a bit...
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うち in this case indicates a period within which an action is happening; so
"inside the time". In English you would probably translate it as "while
still".

While your translation sounds correct, in the Japanese sentence the fact that
the action is unintentional/unconscious gets emphasized a bit more. To bring
that out in the translation, you could maybe say: "It was probably an
unconscious action/action made unconsciously."
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[Goo辞書](http://dictionary.goo.ne.jp/jn/19186/meaning/m0u/) entry #4 under
うち【内】 had this to say:

> ４ （「裡」とも書く。「…のうちに」の形で）物事の行われる状況を表す。「暗黙の―に理解しあう」「会は成功の―に終わる」
>
> 4 (Also rendered 「裡」; Used in the form 「...のうちに」) Denotes the conditions in
> which something is done (*I'll come back to the examples later.)

Although the dictionary for some reason only mentions the adverbial form
「...のうちに」, the adnominal form 「...のうちの」 is also in use, though perhaps with
less occurrence. (e.g.「暗黙のうちの了解」,「知らず知らずのうちのマナー違反」 )

With this in mind, let's look at your sentence 「無意識のうちの行動なのだろう」.

The adnominal 「のうちの」 relates 「行動(an action)」 to 「無意識(unawareness,
unintentional-ness)」 .  
「無意識」 is the state, or condition, within whose notional "boundaries" the 行動
was taken. The action was done, so to speak, in the territory of unawareness.

* * *

Notably, the English preposition _in_ has a very similar meaning to this use
of うちに.

_In_ :

>   2. With reference to circumstances or conditions
>

or

>   4. With reference to physical surrounding, personal states, etc.,
> abstractly denoted
>

(Both cited from [here](http://www.webster-dictionary.org/definition/In).)

To illustrate using the examples from goo辞書:

> 暗黙 **のうちに** 理解しあう ⇔ understand each other **in** silence
>
> 会は成功 **のうちに** 終わる ⇔ the meeting/gathering ends **in** success

In the two examples above, both _~のうちに_ and _in_ describe in what way or under
what circumstances/conditions something happens. However, this does not mean
they are always the best translation for each other. For instance, "tacitly"
would be a better word for「暗黙のうちに」 most of the time.
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