Quoting Big Brother

Perl (191 184 characters)

$_=$$&1?"0
I12321me6T4they,34we
06":"WAR5PEACE6FREEDOM5SLAVERY6IGNORANCE5STRENGTH6";s/\d/("Under the spreading chestnut tree"," sold ",you," and ","here lie "," IS ",".
")[$&]/ge;print

Thanks @core1024 for tips on golfing this.

Java, 338

I can't get it below 338...

class B{public static void main(String[]a){String b="Under the spreading chestnut tree",c="sold ",d="you ",e="and ",f="me.\nT",g="here lie ",h=".\n",i=" IS ";if(Math.random()>.5)System.out.print(b+"\nI "+c+d+e+d+c+f+g+"they, "+e+g+"we\n"+b+h);else System.out.print("WAR"+i+"PEACE"+h+"FREEDOM"+i+"SLAVERY"+h+"IGNORANCE"+i+"STRENGTH"+h);}}

Bit ungolfed:

class B{public static void main(String[]a){String b="Under the spreading chestnut tree",c="sold ",d="you ",e="and ",f="me.\nT",g="here lie ",h=".\n",i=" IS ";
if(Math.random()>.5)System.out.print(b+"\nI "+c+d+e+d+c+f+g+"they, "+e+g+"we\n"+b+h);
else System.out.print("WAR"+i+"PEACE"+h+"FREEDOM"+i+"SLAVERY"+h+"IGNORANCE"+i+"STRENGTH"+h);}}

PHP 179

Inspired by es1024's answer.

<?=strtr(rand()%2?"0
I 1 232 1 me.
T5 they,35 we
0.
":"WAR4PEACE.
FREEDOM4SLAVERY.
IGNORANCE4STRENGTH.
",["Under the spreading chestnut tree",sold,you," and "," IS ","here lie"]);