Yes, US patent numbers are assigned in chronological order with respect to the issue date. The sequence beginning with "1" was established by Patent Act of 1836. The citation is Ch. 357, 5 Stat. 117 (July 4, 1836)

Robert Cogan is right, the patent numbers are chronological in relation to issue date but they don't track the filing date of the patent application that gave rise to the patent. thus a patent application filed in 2005 can give rise to a patent with a lower number than one filed in 2003 simply because the former was accepted more quickly than the latter. in Europe, the patent number is the same as the published application number and so the 2005 application will tend to have a higher number than the 2003 application. Don't pay any attention to it. The numbers simply tell you where to look - when you look, you will find the relevant information. For me, EP-A-2222000, is as helpful as JACS 111: 201-2 (2014), it just lets me know how to find the details.