Myślę, że powinnaś była kupić kurczaka wcześniej, bo teraz w sklepie nie ma mięsa.

Powinnaś is the 2nd person singular feminine form of powinien / powinna / powinno, meaning should / ought to.

So the speaker is talking to one woman or girl.

• to a woman: powinnaś
• to a man: powinieneś

So if the sentence were addressed to a man, it would be:

Myślę, że powinieneś był kupić kurczaka wcześniej...

This structure expresses you should have bought in the past.

• powinnaś kupić can mean you should buy or, depending on context, you should have bought
• powinnaś była kupić makes the past, unrealized obligation much clearer

So this is a very natural way to say that something would have been the right thing to do, but it did not happen.

Because in this pattern, the person is already marked on powinnaś.

The ending -ś already tells us it means you.
The word była is part of the past construction and shows feminine singular, but it does not take the extra -ś here.

So the standard form is:

• powinnaś była kupić
• not powinnaś byłaś kupić

This is a fixed and important pattern to learn.

Because after powinien / powinna / powinno, Polish normally uses an infinitive.

So:

• powinnaś kupić = you should buy
• powinnaś była kupić = you should have bought

The same happens with many other modal-like expressions in Polish.

Because kupić is perfective, and here the speaker means one completed action: the act of buying the chicken.

• kupić = to buy, to complete the purchase
• kupować = to be buying / to buy repeatedly / to buy in a more ongoing or habitual sense

Since the sentence refers to one specific purchase that should have been completed earlier, kupić is the natural choice.

Because kurczaka is the accusative singular form used as the direct object of kupić.

The noun kurczak is masculine animate, and in the singular its:

• nominative = kurczak
• accusative = kurczaka

That is why Polish says:

• kupić kurczaka

Even though the form looks like the genitive, here it is functioning as the accusative.

Wcześniej means earlier.

It is an adverb, and it tells us when the action should have happened.

So:

• kupić kurczaka wcześniej = buy the chicken earlier

A useful thing to notice is that Polish often uses wcześniej even when English would simply say earlier, without needing to spell out an explicit comparison.

Because że introduces the clause that follows I think.

So:

• Myślę = I think
• Myślę, że... = I think that...

In English, that is often optional. In Polish, że is normally used in this kind of sentence.

Both can mean because, but bo is the more everyday, conversational choice.

• bo = common, natural, frequent in speech
• ponieważ = more formal or more written

So in ordinary speech, bo sounds very natural here:

...bo teraz w sklepie nie ma mięsa.

Because w means in, and when it refers to a location with no movement, Polish uses the locative case.

The noun changes like this:

• sklep = shop, store
• w sklepie = in the shop / in the store

So:

• idę do sklepu = I’m going to the store
• jestem w sklepie = I’m in the store

Here it is a location, so w sklepie is correct.

Because nie ma takes the genitive in Polish.

The base form is:

• mięso = meat

But after nie ma, it becomes:

• mięsa

So:

• jest mięso = there is meat
• nie ma mięsa = there is no meat

This is a very common Polish pattern, and learners need to get used to it.

Because the speaker is now talking more broadly about what is available in the store: there is no meat.

That can imply:

• there is no chicken left because the meat section is empty
• or more generally, the store has run out of meat

Using mięsa sounds natural and slightly broader than repeating kurczaka.

Because Polish punctuation normally requires a comma before these kinds of clauses.

• że introduces a subordinate clause
• bo introduces a reason clause

So the commas in:

Myślę, że... , bo...

are standard Polish punctuation.

Yes. Polish word order is quite flexible, and changing it usually changes emphasis, not the core meaning.

For example, you could also say:

Myślę, że wcześniej powinnaś była kupić kurczaka, bo teraz nie ma mięsa w sklepie.

That still means basically the same thing, but the emphasis shifts a little toward earlier.

The original sentence sounds natural and neutral.