UPDATE 1-Chile presidency race seen tied in run-off - poll

(Updates with second round run-off tie seen)

SANTIAGO, June 18 (Reuters) - Chilean billionaire and conservative presidential candidate Sebastian Pinera's lead has narrowed over his ruling center-left coalition opponent ahead of December's election, and they are seen as tied in a likely second-round run-off, a new poll showed on Thursday.

The survey by CEP, or Center for Public Studies, regarded as Chile's benchmark poll, said Pinera of the opposition Renovacion Nacional party would win 37 percent of the vote, compared to 41 percent in its last poll in late December.

That is well short of the outright majority needed to avoid a run-off in an election six months away. Former President Eduardo Frei, who governed the ruling center-left coalition from 1994 to 2000, polled 30 percent, down from 31 percent in the previous CEP poll.

Enriquez-Ominami, a former film producer and left-leaning independent, came in third with 13 percent.

Under election rules, the two candidates with the most votes head into a showdown in January if no candidate wins 50 percent of the vote plus one additional vote in December. In the run-off, the candidate with the most votes wins.

CEP said that Pinera and Frei would be in a technical draw in a two-way second-round run-off. Pinera polled 41 percent against 39 percent for Frei in a simulated vote in which respondents placed their votes in a ballot box.

However in a questionnaire filled out by respondents, both polled 39 percent support.

"In a second round, they are basically tied," said Carolina Segovia, who coordinated the CEP poll.

The CEP poll interviewed 1,505 adults across Chile between May 14 and June 3 and had a margin of error of plus or minus 3 percentage points. (Reporting by Rodrigo Martinez, Writing by Simon Gardner; Editing by Eric Beech)