Amanda Spielman has warned ministers that their plan for more grammar schools sends "a difficult message" to "a lot of people" about social mobility.
Addressing the annual conference of the Association of School and College Leaders (ASCL), Ms Greening said: "We have to recognise that for grammars that in terms of the disadvantaged children that they have, they really do help them close the attainment gap."
Speaking on the BBC World at One programme, Ms Spielman said that she understood that the issue of grammar schools was "very difficult and emotional" for many people.
The focus on social mobility
She went on to say that it also sent "a difficult message" to "a lot of people".
"People are very focused on social mobility, prospects for disadvantaged children," Ms Spielman said. "And it’s clear that not very many disadvantaged children get to go to grammar school, though they tend to do very well when they get there."
Ms Spielman, who took up the post of chief inspector at the start of the year, also addressed the ASCL conference today. As TES reported this morning, she used her speech to announce a major Ofsted investigation into the "scandal" of schools gaming the system in order to improve their own league-table positions.
Speaking truth to power
The chief inspector also indicated that she would be prepared to criticise the government where necessary. She told heads: "Anyone who assumes that the high value I place on evidence and data means that I am reluctant to speak truth to power will find themselves mistaken.
"In fact, it is the use of robust evidence and data that gives Ofsted the authority to challenge, on behalf of the minority of children who are being let down."
Ms Spielman finished by telling schools not to spend too long preparing for her inspectors' visits.
"Ofsted inspections should not be a performance that schools spend hours rehearsing," she said. "Our inspectors are getting better at evaluating whether what we see on inspection is a true reflection of the everyday life of a school.
"And no matter what so-called ‘consultants’ are selling, when school finances are under pressure and workloads are high, running mocksteds is an unacceptable waste of staff time and scarce pupil funding."