Is the word chave the same in Brazilian and European Portuguese?

Yes

The word "chave" is identical in both Brazilian and Continental Portuguese regarding its meaning, spelling, and grammatical function. The only difference is pronunciation. In Brazilian Portuguese, the vowels are typically more open and the rhythm is more melodic (syllable-timed). In Continental Portuguese, the pronunciation is more "closed" and the rhythm is stress-timed, meaning the unstressed final "e" is often reduced or almost silent.

Brazilian Portuguese Examples:

1. Onde estão as minhas chaves? (Where are my keys?)
2. Eu esqueci a chave do carro em cima da mesa. (I forgot the car key on the table.)
3. A chave do sucesso é o trabalho duro. (The key to success is hard work.)
4. Você pode me dar a chave da porta? (Can you give me the door key?)
5. Eu não achei a chave do meu armário. (I didn't find the key to my locker.)

Continental Portuguese Examples:

1. Onde estão as minhas chaves? (Where are my keys?)
2. Esqueci-me da chave do carro em cima da mesa. (I forgot the car key on the table.)
3. A chave do sucesso é o trabalho árduo. (The key to success is hard work.)
4. Podes dar-me a chave da porta? (Can you give me the door key?)
5. Não encontrei a chave do meu cacifo. (I didn't find the key to my locker.)