Check if returned value is not null and if so assign it, in one line, with one method call

Java lacks coalesce operator, so your code with an explicit temporary is your best choice for an assignment with a single call.

You can use the result variable as your temporary, like this:

dinner = ((dinner = cage.getChicken()) != null) ? dinner : getFreeRangeChicken();

This, however, is hard to read.

Same principle as Loki's answer but shorter. Just keep in mind that shorter doesn't automatically mean better.

dinner = Optional.ofNullable(cage.getChicken())
  .orElse(getFreerangeChicken());

Note: This usage of Optional is explicitly discouraged by the architects of the JDK and the designers of the Optional feature. You are allocating a fresh object and immediately throwing it away every time. But on the other hand it can be quite readable.