I was able to get wireless working by upgrading to version 4.4 of the kernel, as chili555 mentioned. As I'm writing, the Ubuntu team is at release candidate 8 of the 4.4 kernel.
To install the newer kernel version, first install Ubuntu (I used 15.10), then download the most recent Ubuntu build from the Ubuntu kernel PPA, move the appropriate
.deb files on a USB drive to your laptop, and install them with
dpkg -i *.deb.
I used v4.4-rc8-wily, but newer versions are released all the time.
See these instructions for general guidance on upgrading to a newer kernel version.
After restarting, I installed the newest versions of the
linux-firmware-nonfree packages I could find. You can find them by searching online for 'ubuntu packages linux-firmware' and 'ubuntu packages linux-firmware-nonfree'.
(I apologize for not posting direct links; apparently I need more reputation points to have more than two URLs.)