He has also played for Mexican sides Pachuca, Leon and Necaxa.
His place in his country's affections was, in fact, assured long ago, after scoring in the under-17 world championships in 1985.
"I scored our first ever goal in a major tournament," Medford said. "It was a beautiful experience."
And qualification for Japan and South Korea, pipping Mexico and the USA to the Concacaf qualifying top spot, was yet another one.
"Three-and-a-half million people in Costa Rica were overjoyed. Now we are desperate to do well for them," said Medford, who is currently battling with a knee injury.
Indeed, it seems he is willing to risk his own health for the chance of more "beautiful experiences".
A doctor has told Medford he could wreck his knee completely unless he undergoes surgery in April and foregoes the chance of a second World Cup appearance.
Medford, though, appears willing to take the gamble.
The man, who after a decade abroad was so keen to return to his homeland that he paid his own £50,000 transfer to cash-strapped Deportivo Saprissa, is just too big a legend to leave behind.