What standard governs the dimensions of SMT chip resistors and capacitors?
The answer may be IEC 60115-8 for resistors, and IEC 60384-21 and IEC 60384-22 for capacitors.

However, further research suggests that the primary source should actually be EIA PDP-100 – if it were up to date. The latest edition of this appears to be from either 1987 or 1992. There's a convoluted history you can dive into at Wikipedia, JEDEC, and ECIA, but the short story is that the EIA is no more, and the EIA standards are now maintained by the ECIA. There is some evidence that a new edition of PDP-100 has been worked on, but there doesn't appear to be much activity right now.