Note:
- As you point out in your own answer, special quoting requirements apply to
choco.exe's /ia parameter.
- However, since you are using
Start-Process, it is not the instructions from the linked page for PowerShell that apply in this case, but the ones for cmd.exe (even though there is no shell involved in this invocation; however, like cmd.exe, console applications themselves generally only understand "..." quoting); that is, your -ArgumentList string must end up containing the following verbatim, which is what the string passed to -ArgumentList below achieves via embedded " characters escaped as `" ("" would work too):
"/D=""C:\Program Files\packagename"""
Start-Process -Wait -FilePath "C:\ProgramData\chocolatey\choco.exe" `
-ArgumentList "install $ChocoPackage -ia `"/D=`"`"C:\Program Files\packagename`"`"`" -y"
Only if you call choco.exe directly from PowerShell do the PowerShell instructions apply ('/D=""C:\Program Files\packagename""'):
& "C:\ProgramData\chocolatey\choco.exe" install $ChocoPackage -ia '/D=""C:\Program Files\packagename""' -y
As for what you tried:
What you passed to -ArgumentList was composed of three directly adjoining string literals in the form " a "' b '" c ", to use a simplified example (i.e., a double-quoted string right next to single-quoted string, right next to another double-quoted string).
However, PowerShell doesn't fully support implicit concatenation of directly adjoining string literals to form a single argument the way that POSIX-compatible shells such as bash do; doing so results in the strings being passed as separate arguments, which caused your problem (Start-Process saw extra positional parameters after -ArgumentList it didn't expect).
To demonstrate the original problem with the simplified example:
PS> Write-Output " a "' b '" c "
a
b
c
That is, Write-Output received string literals " a ", ' b ', and " c " as 3 separate arguments (as implied by their appearing on their own line each).
Only if the first token is unquoted do you get a single string argument composed of it and subsequent quoted tokens:
# *Single* argument, because `a` is *unquoted*.
PS> Write-Output a' b '" c "
a b c
The same applies even if that first unquoted token is a (non-expression) variable reference (e.g., Write-Output $HOME/'folder 1'/"and more"; see this answer for more information
If you do need to reliably form a single string argument from a mix of double-quoted (interpolating) and single-quoted (verbatim) string literals, use (...), the grouping operator, and the + operator for explicit string concatenation:
PS> Write-Output (" a " + ' b ' + " c ")
a b c
