You can enclose the logic in curlies to form a bare block and replace the exit with redo.

I'd prefer to organize the code refs as a real hash like so:

{
    chomp (my $choice = <STDIN>);
    if (exists $codehash{$choice}) {
        &{$codehash{$choice}}; }
    else {
        print "ERROR: Please type in either 1, 2 or 3.\n"; 
        redo; }
}
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