The Catholic Archdiocese of Chicago has tapped an adviser to sell the sprawling lot across the street from its 140-year-old Holy Name Cathedral, in the latest sign of a religious institution selling prime real estate in response to hot property markets.

The Archdiocese has hired Eastdil Secured LLC to market the site, which takes up most of a block, according to Betsy Bohlen, the former McKinsey & Co. partner who became the Archdiocese’s chief operating officer last year. She declined to put a value on the property, but...