Carter Hawley Hale Stores Inc., the largest department store chain in the West, reported a 10.5 percent increase in first-quarter earnings.

Net earnings for the quarter ended May 5 were from $6.1 million (21 cents a share), up from $5.5 million (19 cents) in the same period last year.

The results of this quarter reflect earnings after the acquisition of John Wanamaker, which was purchased on May 3, 1978, after the figures for the year-ago quarter were compiled. First-quarter sales were $486.7 million, up from $375.5 million in the comparable period in 1978.

The firm said that each of the company's three retail groups-department stores, high-fashion speciality stores and specialized merchandising stores-reported higher sales during the quarter compared to last year.

The firm operates 117 stores through its department store divisions. Among some of the stores the Los Angeles-based company operates are Bergdorf Goodman in New York; Neiman-Marcus in the South and Midwest; Sunset House, a novelty mail-order and giftshop business; and the Walden Book Co.

Dayton Hudson Corp., a retail store chain, earned 22 cents a share in its first quarter ended May 5, up from 4 cents a year earlier on a rise in sales to $656.75 million from $566.99 million. Net income rose to $5.16 million from $930,000.