You can use a \@labels trick (as in Phil Hirschhorn's answer to “Avoiding a line break at the beginning of an enumerate”). Here's the result:

There are two ways you can use this. The first is by manually putting a \thmenumhspace{-1em} before each \begin{enumerate} inside a theorem:
\documentclass{article}
%\usepackage{amsthm,enumitem,thmtools}% works with or without
\newtheorem{Theorem}{Theorem}
\makeatletter
\newcommand{\thmenumhspace}[1]{\sbox{\@labels}{\unhbox\@labels\hskip#1}}
\makeatother
\begin{document}
\begin{Theorem}
On the other hand, this one has only one claim.
\end{Theorem}
\begin{Theorem}\thmenumhspace{-1em}
\begin{enumerate}
\item First claim
\item Second claim
\end{enumerate}
\end{Theorem}
\end{document}
With a little more work, this can be automated, hopefully without any side effects (this time, you need amsthm for it to work correctly):
\documentclass{article}
\usepackage{amsthm,enumitem,thmtools}% needs amsthm
\newtheorem{Theorem}{Theorem}
\makeatletter
\newcommand{\thmenumhspace}[1]{\sbox{\@labels}{\unhbox\@labels\hskip#1}}
\let\original@item\item
\newcommand{\RedefineItem}{%
\def\item{\let\item\original@item\thmenumhspace{-1em}\original@item}
}
\let\original@Theorem\Theorem
\def\Theorem{
\@ifnextchar[{\Theorem@Opt}
{\Theorem@NoOpt}
}
\def\Theorem@Opt[#1]{%
\@ifnextchar\begin{\RedefineItem\original@Theorem[#1]}%
{\original@Theorem[#1]}%
}
\def\Theorem@NoOpt{%
\@ifnextchar\begin{\RedefineItem\original@Theorem}%
{\original@Theorem}%
}
\makeatother
\begin{document}
\begin{Theorem}
On the other hand, this one has only one claim.
\end{Theorem}
\begin{Theorem}
\begin{enumerate}
\item First claim
\item Second claim
\end{enumerate}
\end{Theorem}
\begin{Theorem}
On the other hand, this one has only one claim.
\begin{enumerate}
\item First claim
\item Second claim
\end{enumerate}
\end{Theorem}
\begin{Theorem}[Title]
\begin{enumerate}
\item First claim
\item Second claim
\end{enumerate}
\end{Theorem}
\begin{Theorem}[Title]
On the other hand, this one has only one claim.
\begin{enumerate}
\item First claim
\item Second claim
\end{enumerate}
\end{Theorem}
\end{document}
`. Feel free to put the+s back in. – Martin Scharrer♦ May 5 '11 at 9:24