There is a couple in my neighborhood.

They are poor and they have no children.

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Do we have to use 'there is' instead of 'there are'? In the second sentence 'they' refers to 'a couple'.
Do we have to use 'they'?

The word "couple" is a collective noun, like family. Each word is made up of more than one person, but the word itself is singular. However, "they" then refers to the people in that group.