diff --git a/babel.config.js b/babel.config.js
index 0c8d5affcd..da3942c6da 100644
--- a/babel.config.js
+++ b/babel.config.js
@@ -22,6 +22,13 @@ module.exports = {
         "@babel/plugin-proposal-object-rest-spread",
         "@babel/plugin-proposal-optional-chaining",
         "@babel/plugin-proposal-nullish-coalescing-operator",
+
+        // transform logical assignment (??=, ||=, &&=). preset-env doesn't
+        // normally bother with these (presumably because all the target
+        // browsers support it natively), but they make our webpack version (or
+        // something downstream of babel, at least) fall over.
+        "@babel/plugin-proposal-logical-assignment-operators",
+
         "@babel/plugin-syntax-dynamic-import",
         "@babel/plugin-transform-runtime",
     ],