Will a grille out of 2001 Chevy fit in 1997 Tahoe?

No, a grille from a 2001 Chevy Silverado or Suburban (assuming that's what you mean by "Chevy") will almost certainly not fit a 1997 Tahoe. The body styles and grille dimensions changed significantly between those years. Even if the overall size seems similar, the mounting points and shape will likely be incompatible.