No saldré del gallinero hasta que la última gallina se calme.

Saldré is the 1st person singular future of salir: I will leave / I won’t leave.

So:

• saldré = I will leave
• no saldré = I will not leave

In this sentence, the speaker is talking about a future action that depends on something else happening first.

In Spanish, de + el contracts to del.

So:

• de el gallinero → del gallinero

This is a standard contraction, just like:

• a + el → al

But note that this only happens with the article el, not with la:

• de la casa = correct
• del casa = incorrect

Gallinero means henhouse or chicken coop.

It comes from:

• gallina = hen
• gallinero = the place where hens/chickens are kept

So del gallinero means out of the chicken coop / from the henhouse.

Hasta on its own usually means until / up to before a noun or time expression:

• hasta mañana = until tomorrow
• hasta el lunes = until Monday

But when it is followed by a clause with a verb, Spanish normally uses hasta que:

• hasta que llegue = until he/she arrives
• hasta que termine = until it ends

Here, what follows is a whole clause:

• la última gallina se calme

So hasta que is required.

Because after hasta que, Spanish usually uses the subjunctive when the action is in the future or has not happened yet.

Here, the hen has not calmed down yet. The speaker is saying they will not leave until that future moment happens.

So:

• hasta que ... se calme = correct
• hasta que ... se calma = not correct here

Compare:

• No saldré hasta que se calme. = I won’t leave until it calms down.
• Esperé hasta que se calmó. = I waited until it calmed down.

In the second sentence, the calming-down already happened in the past, so the indicative is used.

Calme is the present subjunctive form of calmarse for él / ella / usted.

The verb here is really calmarse, which means to calm down.

Conjugation:

• yo me calme
• tú te calmes
• él/ella se calme

Since la última gallina is she/it, the form is se calme.

Because the verb used here is calmarse, not just calmar.

• calmar = to calm something/someone
• calmarse = to calm down

So:

• Calmo a la gallina. = I calm the hen.
• La gallina se calma. = The hen calms down.

In your sentence, the hen is the one changing state by herself, so Spanish uses the pronominal form se calme.

La última gallina means the last hen.

• la = the (feminine singular)
• última = last (feminine singular)
• gallina = hen (feminine singular)

Both the article and the adjective must agree with gallina, which is feminine singular.

So:

• el último gallo = the last rooster
• la última gallina = the last hen

In Spanish, many adjectives can come after the noun, but some common ones, including último, often appear before the noun when they have a more natural, fixed, or descriptive meaning.

So:

• la última gallina = the last hen

This is the most natural order here.

If you changed the order to la gallina última, it would sound unusual in normal speech.

Yes. That version is also grammatical.

Both mean the same thing:

• ...hasta que la última gallina se calme
• ...hasta que se calme la última gallina

The difference is mainly word order and focus.

• la última gallina se calme puts the subject first
• se calme la última gallina puts a bit more attention on the action happening

The original version is very clear and natural.

No. It is a very natural way, but not the only one.

Possible alternatives include:

• No voy a salir del gallinero hasta que la última gallina se calme.
• No salgo del gallinero hasta que la última gallina se calme.

Differences:

• No saldré = simple future, slightly firmer or more formal in tone
• No voy a salir = very common spoken future
• No salgo can sometimes be used for a future plan in spoken Spanish, but here it may sound a bit less neutral than no saldré

The original sentence is perfectly natural.

A rough pronunciation guide would be:

No sal-dré del ga-lli-NÉ-ro AS-ta ke la UL-ti-ma ga-LLI-na se KAL-me

A few useful points for Spain Spanish:

• saldré has stress on the last syllable: -dré
• gallinero has stress on -ne-
• última has stress on úl-
• gallina usually has the ll sound pronounced like y in most of Spain today
• que sounds like keh

A more approximate English-style guide:

noh sahl-DREH del gah-yee-NEH-roh AHS-tah keh lah OOL-tee-mah gah-YEE-nah seh KAHL-meh

It breaks down like this:

• No saldré = I will not leave
• del gallinero = the chicken coop / the henhouse
• hasta que = until
• la última gallina se calme = the last hen calms down / has calmed down

So the pattern is:

No + future verb + place + hasta que + subjunctive clause

This is a very useful structure in Spanish:

• No me iré hasta que termine. = I won’t leave until it finishes.
• No abriré la puerta hasta que llegues. = I won’t open the door until you arrive.