Are there chiral compounds that don't rotate plane-polarized light? I know that meso compounds have chiral centers but don't rotate plane-polarized light, and I know that there can be non-traditionally chiral compounds (e.g. ones with large substituents that prohibit much rotation around single bonds) that can still rotate light, but I haven't been able to find any molecules that are chiral but don't rotate plane-polarized light (or rotate it impossibly little). I'm imagining something like an enantiomeric pair connected by one single bond with a slight modification to one that makes it have similar optical activity but not actually be identical (so the final molecule is indeed chiral), but I don't know exactly how to make it work.
Good question.
There's a phenomenon named cryptochirality[1] (meaning “hidden chirality”), when a compound, though chiral, has practically unmeasurable optical rotation activity.

It can happen to molecules with chiral center(s) bearing very similar substituents. (So, no tricks with bonded slightly modified enantiomeric pairs are needed.)

An example is 5-ethyl-5-propylundecane $\ce{CH3[CH2]5-\overset{$*$}{C}(CH2CH3)(CH2CH2CH3)-[CH2]3CH3}$,[2] don't call it “butyl(ethyl)hexyl(propyl)methane”, found e.g. in beans. Its specific rotation is $[\alpha] &lt; 0.001$.

Another, more common example are fats, i.e. triglycerides, $\ce{RCOOCH2\overset{$*$}{C}H(OCOR')CH2OCOR''}$,[1] if containing e.g. only palmitic, oleic and similar long acyls, optical rotation is not demonstrable.[3]

(Related topic is chirality in polymers, see e.g. Q: Chirality on Carbon of PVC molecule.)



References:


Mislow K. &amp; Bickart P.: An Epistemological Note on Chirality. Israel Journal of Chemistry 15, 1–6 (1976)
Wynberg H., Hekkert G.L., Houbiers J.P.M. &amp; Bosch H.W.: The Optical Activity of Butylethylhexylpropylmethane. Journal of the American Chemical Society 87, 2635–2639 (1965)
Schlenk W.: Synthesis and analysis of optically active triglycerides. Journal of the American Oil Chemists’ Society 42, 945–957 (1965)