I see with some regularity claims that there’s no word that rhymes with “orange,” “silver,” “month,” or other words. Recently someone on the American Dialect Society email list also included “chamber” as a word for which there is no rhyme in English.
Most of those “nothing rhymes with” chestnuts are easily answered because the queries are poorly phrased. Maybe taking advantage of poor phrasing seems like a loophole that defeats the spirit of the questions, but I think that when puzzles or challenges are presented—when someone is pitting their factoid knowledge against yours—then loopholes are just begging to be exploited. For example:
Rhyming with “chamber” is easily done because the question is rarely posed in such as a way as to forbid words that include “chamber” in their makeup. Sure, that’s a rule for poetry and lyrics, but as far as I’m concerned, if you simply claim “there’s NOTHING that rhymes with chamber,” then these answers are perfectly acceptable—because they do rhyme in a most exact way. There are many more hyphenated or compound forms rhyme, too.
If you meant to exclude rhymes that include exact forms of the word to be rhymed, then you should say so.
antichamber (variant of above)
Orange has several rhymes, as long as you are content with rhyming only the final syllable. In my idiolect of American English, the following can rhyme with “orange,” depending on how careful my speech is, since the central schwa usually vanishes in “orange.” I tend to pronounce it as or-RUNJ or ornj. If you meant “there’s no single word that rhymes with the ENTIRE word ‘orange’” then you should say that, too.
Some would add “syringe” to the list, but it doesn’t rhyme for me: sir-RINJ or suh-RINJ.
For words that rhyme with “silver,” besides hyphenated forms there are:
There are many words that rhyme with month, without using a loophole:
A wildcard search of OED online is quite useful in coming up with these sorts of answers, particularly since the queries usually don’t specify non-archaic, non-obsolete words (another loophole).