They may be dangerous words to use given the history of the Israeli-Palestinian conflict, but once again they are being uttered and by no lesser person than the world's most powerful woman - the US Secretary of State, Condoleezza Rice.
"This is a time of opportunity and a time we have to seize," she said at the start of a two-day visit to the Middle East for talks with Israeli and Palestinian leaders.
The words were repeated many times throughout her visit, culminating in an appeal to both sides to make the "maximum efforts to give this chance for peace a real chance".
Palestinian and Israeli leaders have spoken of a historic opportunity
Thus the stage has been set for Tuesday's summit between Israeli Prime Minister Ariel Sharon and the recently-elected Palestinian leader, Mahmoud Abbas.
The two men are due to meet in the Egyptian resort of Sharm al-Sheikh for a total of five hours.
The host, Egyptian President Hosni Mubarak, and King Abdullah of Jordan will be with them.
So should anyone dare to hope that this summit will mark the beginning of a new phase of serious negotiations to end the protracted conflict in the Middle East?
In recent months one funeral, two elections and a continuing promise of withdrawal seem to have given grounds for renewed optimism.
For the US and Israeli governments, the death of veteran Palestinian leader Yasser Arafat last November removed a major obstacle to peace.
Palestinian forces train to take over in West Bank towns
They did not believe he would launch a serious crackdown on the Palestinian militant groups responsible for numerous attacks on Israeli targets.
However Mr Abbas, who was elected last month, has already succeeded in negotiating an informal ceasefire with the main militant organisations, Hamas and Islamic Jihad.
The violence has now subsided in what is a critical first step towards reviving meaningful negotiations.
Far away in Washington, the re-election of President George W Bush also appears to have brought a change in approach.
After letting the Israeli-Palestinian conflict slip far down his agenda, President Bush has now indicated he is changing his administration's priorities.
Ms Rice's visit to the Middle East so soon after confirmation in her new post is meant to signal renewed US commitment to helping to resolve the conflict - with the ultimate goal of creating a viable Palestinian state.
And finally there is the plan pushed through by the Israeli prime minister to withdraw all Israeli settlers and military forces from the occupied Gaza Strip later this year - a significant move by a leader better known for his hawkish policies.
Bridging big issues
This more conducive overall environment has helped bring about the Sharm al-Sheikh summit, which will be the highest level meeting between the Israelis and Palestinians for four years.
Ever since last week's announcement that the summit would take place, there have been intensive negotiations behind the scenes between the two sides.
Israel has pledged to release 900 Palestinian prisoners
There are some indications of goodwill. The Israelis have pledged to release 900 Palestinian prisoners and to gradually hand over control of five towns in the occupied West Bank to the Palestinian security forces.
A formal declaration of an end to the violence would be a crucial step forward.
But it would only be the first of many required to bring about lasting peace.
Among those steps are the really substantive issues such as the Israeli settlements in the occupied West Bank, the status of East Jerusalem and the right of return of Palestinian refugees to lands which are now in Israel.
On these, the two sides remain far apart.