Except in Ubuntu 10.04 LTS Lucid Lynx, and in Precise (the development version which will eventually be released as Ubuntu 12.04 LTS Precise Pangolin), the Ubuntu updates to chromium-browser 15 have not yet been released, but are still undergoing testing in -proposed (source: https://launchpad.net/ubuntu/+source/chromium-browser). See https://help.ubuntu.com/community/UbuntuUpdates for details about the different repositories that provide newer versions of software in Ubuntu, and https://wiki.ubuntu.com/Testing/EnableProposed for information about the -proposed repositories.
I would encourage you to search and see if the problem you are having has been reported, and if it hasn't been, to report it. Please make sure to read https://help.ubuntu.com/community/ReportingBugs carefully first. Then, to file the bug, either run "ubuntu-bug chromium-browser" or invoke ubuntu-bug with the PID of the currently running chromium-browser process (this will make sense after you read ReportingBugs). Make sure to describe the problem clearly and fully in your bug report. After filing your bug, you should post about it in bug 881786; if your bug is considered to qualify for a SRU, it might cause the still-proposed versions to be delayed until the problem is fixed.
If you're running Ubuntu 10.10 Maverick Meerkat, Ubuntu 11.04 Natty Narwhal, or Ubuntu 11.10 Oneiric Ocelot, then you can downgrade from chromium-browser 15 to chromium-browser 14, as major version 14 still still available through the -updates repository (or the release repository in Oneiric). You might find that the easiest way to do this is in the Synaptic Package Manager (which itself can be installed in the Software Center--the package is called: synaptic). Or you can use apt-get from the command-line to perform the downgrade; for example, on an Ubuntu 11.10 Oneiric Ocelot system, you could run "sudo apt-get install chromium-browser=14.0.835.202~r103287-0ubuntu1" (without the quotes). See the apt-get manual page for details. If you are running one of these systems, then chromium-browser was upgraded from the -proposed repository, so you can prevent it from being updated further until the version 15 packages have underwent further testing and been released for general use by disabling that software source or, better, by using pinning (as explained in EnableProposed).
If you're running Ubuntu 10.04 LTS Lucid Lynx, or Precise, the above method will not work, but you might still have the .deb package for major version 14 of chromium-browser in your /var/cache/apt/archives folder. If you don't, then you can see if it's still present at http://archive.ubuntu.com/ubuntu/pool/universe/c/chromium-browser/. It probably is, at least if you act fast, but you should check your /var/log/dpkg.log file to see what the version was on your machine to ensure you get the right one, because if you get the wrong one it could be for a different Ubuntu release, and subtle problems could potentially occur. You should also make sure to get the version for the right architecture, where i386 is for 32-bit Ubuntu systems and amd64 is for 64-bit Ubuntu systems, irrespective of whether your processor is actually manufactured by Intel or AMD. If it's not there, then you could see if it's still on Launchpad by subtituting the old version string (from /var/log/dpkg.log) into the URL https://launchpad.net/ubuntu/+archive/primary/+files/chromium-browser_15.0.874.106~r107270-0ubuntu0.10.04.1_i386.deb (for a 32-bit system) or https://launchpad.net/ubuntu/+archive/primary/+files/chromium-browser_15.0.874.106~r107270-0ubuntu0.10.04.1_amd64.deb (for a 64-bit system).
Please note that if you do manually downgrade chromium-browser, you might need to perform a similar procedure to downgrade related packages, i.e., one or more of the following (probably not the -dbg packages, as you likely do not have them installed): chromium-browser-dbg, chromium-browser-inspector, chromium-browser-l10n, chromium-codecs-ffmpeg-dbg, chromium-codecs-ffmpeg-extra-dbg, chromium-codecs-ffmpeg-extra, chromium-codecs-ffmpeg-nonfree-dbg, chromium-codecs-ffmpeg-nonfree, and chromium-codecs-ffmpeg.
Finally, please note that chromium-browser (Chromium) and Google Chrome are separate applications--the instructions in this post apply to Chromium, which is probably easier to downgrade.
If you attempt to follow these procedures and have difficulty, I'd be please to provide additional assistance (please go ahead and post a comment or comments describing the difficulties).