After long and deep research, I can say definitively, the EGG has it:

#! perl -slw
use strict;
use List::Util qw[ shuffle ];

my $string = join '', shuffle +('A' .. 'Z')x2;;

while( $string = join'', shuffle split '', $string ) {
    printf( STDERR "\r$string" );
    $string =~ s[(CHICKEN|EGG)][>>>$1<<<]
        and die "\n\n$1 came first\n$string\n\n(Selfish lover?)\n";
}

__END__
C:\test>junk1
OEQOLHRDFUWDXPTZBYVLTNWKFBVJSRMAEGGNUQIAXCSZCKIHJPMY

EGG came first
OEQOLHRDFUWDXPTZBYVLTNWKFBVJSRMA>>>EGG<<<NUQIAXCSZCKIHJPMY

(Selfish lover?)

C:\test>junk1
MWZCSLUKEATQYTHOWEGGMVPQYVRRJXBUAKXNDDHFPZJISNOCFBLI

EGG came first
MWZCSLUKEATQYTHOW>>>EGG<<<MVPQYVRRJXBUAKXNDDHFPZJISNOCFBLI

(Selfish lover?)

C:\test>junk1
BZPUIEEGGONAQRWOJFKDHDYCXUFBLWZHYMMVXSISTTJAQKNPVRCL

EGG came first
BZPUIE>>>EGG<<<ONAQRWOJFKDHDYCXUFBLWZHYMMVXSISTTJAQKNPVRCL

(Selfish lover?)
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