It's a Montello. Very nice frame to have.

the investment cast bottom bracket and lack of chainstay bridge mean it is not a Treviso but the higher level Montello. As T-Mar has already said.

Whatever you do, DO NOT powdercoat this frame.

Yes, chrome that is not glossy was originally painted over. My 1984-ish Treviso is totally chromed but the chrome only looks good where it was meant to be shown.