First of all, I think you should not do this, because this gives you a lonely footnote.
This having said, here is how you can achieve it. But you have to mess a little with internals of the achemso package.
First alter the symbols for the footnotes (I don't know if this has any side effects):
\renewcommand*{\acs@author@fnsymbol@symbol}[1]{%
\ifcase #1 *\or
{}\or
\dagger\or
\ddagger\or
\P\or
\S\or
\|\or
\bot\or
\#\or
@\or
\triangle\or
\nabla
\fi
}
Now the symbol for the first affilation has vanished, but you still have two delete the comma, that was originally between the two symbols. This can be done with
\renewcommand*\acs@author@affil@alt@aux{%
\expandafter\acs@affil@marker@cnt
\csname @author@altaffil@\@roman\@tempcnta\endcsname\relax
\advance\acs@affil@marker@cnt\acs@affil@cnt\relax
\advance\acs@affil@marker@cnt\acs@footnote@cnt\relax
\protected@edef\acs@author@footnotes{%
\acs@author@footnotes
{}%
\acs@author@fnsymbol{\acs@affil@marker@cnt}%
}%
}
So the final MWE looks like:
\documentclass{achemso}
\makeatletter
\renewcommand*{\acs@author@fnsymbol@symbol}[1]{%
\ifcase #1 *\or
{}\or
\dagger\or
\ddagger\or
\P\or
\S\or
\|\or
\bot\or
\#\or
@\or
\triangle\or
\nabla
\fi
}
\renewcommand*\acs@author@affil@alt@aux{%
\expandafter\acs@affil@marker@cnt
\csname @author@altaffil@\@roman\@tempcnta\endcsname\relax
\advance\acs@affil@marker@cnt\acs@affil@cnt\relax
\advance\acs@affil@marker@cnt\acs@footnote@cnt\relax
\protected@edef\acs@author@footnotes{%
\acs@author@footnotes
{}%
\acs@author@fnsymbol{\acs@affil@marker@cnt}%
}%
}
\makeatother
\title{Title}
\author{Author 1}
\affiliation{ABC}
\author{Author 2}
\altaffiliation{X}
\author{Author 3}
\affiliation{ABC}
\begin{document}
\end{document}