Split-like environment inside cases environment

Well, I'd follow amsmath's suggestion to use aligned instead of split:

\documentclass{article}
\usepackage{amsmath}

\begin{document}
\[
  \text{left hand side} =
  \begin{cases}
    \!\begin{aligned}%[b]
       & \text{a very long expression} \\
       & + \text{that continues on the next line}
    \end{aligned}           & \text{1st condition} \\%[1ex]
    \text{short expression} & \text{2nd condition}
  \end{cases}
\]
\end{document}

Does this yield the output you want? (Note that the \! in front of aligned is needed since that environment adds a \, we have to cancel out.)

EDIT: If you want to achieve alignment and spacing as Niel suggests (@Niel: I would want that; good catch), then just remove the two % in the code.

Here is an alternative construction to Hendrik's, which aligns the 1st condition with the bottom-most line of the long expression (which I would suggest as good practise generally for readability). I also add vertical space between the two formulae to make it easier to separate the two visually.

\documentclass{article}
\usepackage{amsmath}

\begin{document}
\[
  \text{left hand side} =
    \left\{
    \begin{aligned}
       & \text{a very long expression} \\
       & + \text{that continues on the next line} && \text{1st condition}
    \\[1ex]
       & \text{short expression}                  && \text{2nd condition}
    \end{aligned}
    \right.
\]
\end{document}

I omit the cases environment here, as all of the alignment work that it does is now better performed by aligned. The alignment tabs are chosen to get uniform alignment of the conditions, and left-alignment for everything involved; they can be changed to obtain right-alignment where desired.