Officials believe it has been so successful over three years in seven primary schools in the Northfield area of the city that it should be extended across the city, if the money can be found.
And a small-scale research investigation concluded the project had shown such promise that a new specialist should be introduced into primary schools - the visiting chess coach.
A report to Aberdeen's education committee on Monday by Pete Hamilton, the council's community learning and development manager, noted: "Anecdotal evidence indicated that the project produced demonstrable results in relation to improved behaviour at school, improved learning, enhanced parental involvement and active citizenship.
"The research report confirms this and points to chess as an important tool in improving attainment."
Mr Hamilton suggested the secret of the contribution made by chess to learning could be that a personal code of conduct is central to chess play and therefore is a particular benefit to youngsters experiencing learning difficulties or mood swings, or both.
The researchers state: "Chess play assists the learning of 'how to learn'
and creates a desire to learn, alongside increased motivation and the will to use knowledge."
One father told the researchers who looked in detail at the out-of-school hours project that it had provided "a gift for life". They found that, not only did chess make a contribution to school life, it helped build chess-playing family and community networks.
The initiative was extended from Northfield to include schools in the St Machar area of Aberdeen, involving 350 pupils. Its success was such that P4 pupils in 10 primary schools participated in tournaments up to international level. At the end of the third year, 38 children had appeared in the Scottish list of graded players.
The research looked in depth at a P4 class and administered a pre-test and post-test assessment of pupils' improvement in word recognition, reading, spelling, comprehension, arithmetic and social-behavioural adjustment.
The conclusion was that "chess makes a difference" to reading, spelling and comprehension, with a particularly positive impact on social and behavioural problems. Among other findings:
* The chess-playing family became an educational resource, with children gaining access to a chess set, PC and chess software, books and library membership.
* The development of intergenerational chess play between parent and child and grandparent and child generated a new period of quality time at home.
* Children developed self-regulated learning through voluntary study and chess play practice, which helped problem-solving.
The research study, sponsored by the Scottish Executive Education Department, concluded: "Substantial funding for chess development in Scotland's primary schools could improve literacy, numeracy and the confidence of pupils who require learning support."
It added: "The introduction of chess coaching to the primary school curriculum will have major implications for the teaching profession, continuing professional development, pupil support, parental involvement and the role of the classroom assistant."
The report acknowledges that "chess, like all educational initiatives, cannot be a substitute for social policy measures that tackle the material poverty of low income and a long working day for many parents. It can, however, contribute to children's personal growth and resilience in circumstances of poverty."
Meanwhile the search is on for more secure funding, which so far has come from the lottery and the council. Officials say they need pound;46,500 of core funding to pay for a full-time chess development officer and six part-time assistants.