My friend and I are having a big argument over this, but it may sound kind of stupid.

She said
"Red Hot Chili Peppers are the greatest band ever."

But should it be "is" instead of "are" since it is only one band?

I would say they 'are' the greatest band.
Other opinions?
Actually, it's a good question and we went over it not so long ago. And there are no stupid questions here. I heard it say once that "those who ask do not err" (literal translation from Spanish).

"Band" is a collective noun as people, family, team, company, etc. In general terms, some collectives are considered singular when we refer to them impersonally. For instance:

Red Hot Chili Pepers is a rock band of the 1990s.
Alianza Lima is a Southamerican soccer team founded in 1901.
The average family has two children nowadays.

But when you talk about a certain band, family or team which is your family or your favorite band or team, the plural form is chosen to express "the persons in the group". Compare:

Red Hot Chili Pepers are performing this weekend and I won't miss it.
Alianza Lima are playing great this season. Hope they win the championship.
My family are of great importance for me. I wouldn't do without their support.

Hope this helps! Emotion: smile