What was the first anime that used a split-cour format? Split-cour airing format is a noticeable trend in the anime industry recently. Unlike most multi-season shows that are aired two or more seasons in succession, split-cour shows have a break in between that usually lasts 3 months (1-cour). However, these cours are produced  as a single product over the course of several months, not two separate anime, per se. For more information on cours and split-cours, this question might help.

Recent examples of anime that followed this format are:


Space Dandy - Winter 2014 [break: Spring] Summer 2014
Hitsugi no Chaika - Spring 2014 [break: Summer] Fall 2014
Aldnoah.Zero - Summer 2014 [break: Fall] Winter 2015
Tokyo Ghoul - Summer 2014 [break: Fall] Winter 2015


Some upcoming anime that are announced to be split-cour are Durararax2, F/SN UBW, and the Grisaia VN franchise, though I'm not really sure. Anyway, as the title states: I want to know what was the first anime that used this format of having a 3-month break in between cour/s.
Based on an AniDB search (details below), I'd wage that first such series was Fate/Zero. It started airing on 02.10.2011, had 1 cour break after episode 13 on 25.12.2011, resumed on 06.04.2012 and finished on 24.06.2012.

I ran an advanced search based on following criteria:


( ) characters in title (AniDB marks cours by putting year date in
parentheses)
must be a TV Series
between 10 and 28 episodes (your definition, as I understand it, requires "regular" cour formats)
first episode already aired


Because of deficiencies in AniDB search engine, I could not specify several useful indicators, such as sequel-prequel relation. So I sorted results by air date and examined each individually.

There are older series that aired with a split, but you requested it to be exactly 1 cour (3 months) long. Notably, Mobile Suit Gundam 00 is described by Wikipedia as having been planned from start to end before airing:


  The staff, consisting of over 300 people, spent roughly two years planning the series.


However, the split took 2 cours, from 29.03.2008 to 05.10.2008. If not for the 3 months condition, I'd say that this was indeed first series to air in split-cour format.

Another case is Major, which also had longer split (from 10.06.2006 to 06.01.2007) yet aired before Gundam 00. However, at the time of airing, it was not a "finished product" but ongoing adaptation of still unfinished manga.