Given a second chance after a catastrophic failure last year, an American Delta rocket yesterday carried into orbit the first communications satellite that will serve as a telephone and television link among the nations of Western Europe.

The European Space Agency's Orbital Test Satellite 2 was flown from Cape Canaveral into stationary orbit 22,300 miles over the West African country of Gabon, where it will stay for the next six or seven years relaying telecasts among the nations of the European Broadcast Union and carrying as many as 7,000 telephone calls at any one time.

The 1,100-pound satellite raced away from Cape Canaveral at 6.59 p.m. EDT, powered into space by nine solid-rocket engines stacked in a circle around the main liquid-fueled motor of the Delta rocket.

The three-stage Delta carried the satellite into a parking orbit 111 miles high at 7:08 p.m., then boosted the ESA satellite into an orbit 22,300 miles above the earth where it matches the rotation of the earth, fixed in the same place to serve as a communications relay.

The successful launch follows the catastrophic failure last September of an identical satellite launced from Cape Canaveral. Fifty-four seconds after a Delta rocket lifted the first setellite into the sky, it blew up and destroyed the $42 million spacecraft.

The stallite orbited yesterday by the U.S. Delta rocket was the last of two satellites the European Space Agency had developed and built for $110 million. Had yesterday's launch failed it would have been two years before ESA could attempt another one. A third satellite would have been built with the $50 million paid to ESA by Lloyds of London under and insurance agreement reached between the two parties after last September's failure.

The satellite launced yesterday is the forerunner of the European Communications Satellite, due to be put into orbit in 1981 to provide the equivalent of 17,000 one-way telephone circuits across Western Europe and the Mediterranean region embracing most of North Africa.

The ECS will also serve as a relay station for European television broadcasts now exchanged by most of the countries of Western Europe by ground-based microwave relay stations. That method of television exchange is considered cumbersome and crude and costs the nations making up the European Broadcast Union between $40 million and $50 million a year.

By 1983, the West European consortium hopes to have a pair of European Communications Satellite in stationary orbit, one for operational use and the other to hanle the overflow of peak traffic and for backup in case the other fails. Orbital lifetime of the satellites is expected to be at least seven years.