On the computer containing your bookmarks:
Click the 3 dots at the top right of Chrome, then hover over “Bookmarks” and choose “Bookmark manager”
Click the 3 dots at the top right of the Bookmarks page, then click “Export bookmarks”
Save the bookmarks HTML file to your computer. Then transfer the file to your new computer by uploading it to Dropbox, emailing it to yourself, or transferring it with an external drive/flash drive.
On the new computer:
Click the 3 dots at the top right of Chrome, then hover over “Bookmarks” and choose “Import bookmarks and settings”
Change the drop-down menu to "Bookmarks HTML file", then choose the file that you transferred from the other computer.
The bookmarks may import into an “Imported” folder on the bookmarks bar. You can click and drag bookmarks out of that folder to re-organize them.