Chinchilla, a career politician from the ruling party, pledges to continue Arias’s moderate free-market policies that brought Costa Rica into the Central American Free Trade Agreement with the United States.
He also initiated trade relations with China after a 63-year association with Taiwan.
Otto Guevara, the anti-taxation Libertarian contender, promises to lower taxes, dismantle monopolies and adopt the US dollar as the country’s currency.
Like Guevara, Otton Solis is an opposition candidate, but he represents the country’s centre-left.
Six other candidates are also running in a race that will again test the popularity of the PLN, which has dominated politics in Costa Rica for the past six decades.
At least 200 international observers, including members of the Organisation of American States, are due to oversee the elections.
Costa Rica enjoys the highest standard of living in Central America and is renowned for not having an army and its role in ending the Cold War-era civil wars that wracked its neighbours.
The country is also Central America's oldest democracy with a record of 60 years of democratic elections.