The concrete and steel arch will eventually cover the remains of the reactor which lost its roof in a catastrophic explosion in 1986.
The blast sent a plume of radioactive material into the air, triggering a public health emergency across Europe.
The shield is designed to prevent further radioactive material leaking out over the next century.
It measures 275m (900ft) wide and 108m (354ft) tall and has cost $1.6bn (Â£1.3bn) to construct.
The European Bank for Reconstruction and Development (EBRD), which is leading the project, describes the arch as the largest moveable land-based structure ever built.
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It began moving on Monday using a system of hydraulic jacks and will take about five days to be put in its final position.
Work will then begin to safely dismantle the reactor, which has been sealed inside a so-called sarcophagus, and to secure the huge amount of radioactive material still inside.
Experts fear that if parts of the reactor collapse inside the sarcophagus, further radioactive material could be released.
The shield, known as the New Safe Confinement, had to be built away from the scene of the accident as the radiation immediately above the reactor is still too intense.
Ukraine's ecology minister, Ostap Semerak, said the start of the operation to cover the reactor was "the beginning of the end of a 30-year long fight with the consequences of the 1986 accident".
"The credit for construction of this one-of-a-kind technological structure goes to an expert team of engineers and builders," he said.
The meltdown and explosion at the Soviet-era plant was the worst nuclear disaster in history, spewing a cloud of radioactive material that drifted into other parts of the then-USSR, including Russia and Belarus, and northern Europe.
The number of people killed remains disputed. A 2005 report by the UN-backed Chernobyl Forum said that fewer than 50 people had died as a result of exposure to radiation, most of them workers killed immediately after the disaster, but some survived until as late as 2004.
The forum estimated that up to 9,000 people could eventually die from radiation exposure, although Greenpeace claims the figure could be as high as 93,000.
Work has begun at Chernobyl in Ukraine to move a giant shield over the site of the world's worst nuclear accident.