Geico Corp., the big Chevy Chase insurance holding company, is planning a belated entry into the booming money market mutual fund industry.

Company Chairman John J. Byrne revealed the decision yesterday, stating that although Geico is "entering the marketplace with this product somewhat later than our competitors, there is a strong demand for money market funds, and it appears to be a logical expansion of our customer services."

The new investment company, to be called Government Securities Cash Fund, is expected to be offered to the public about mid-December and will invest exclusively in such short-term government instruments as Treasury bills.

Established as a major financial services business only five years ago, money market mutual funds have grown steadily.

The funds have given savings institutions fits and have benefited from high yields to investors during a period of record inflation. Most of the funds now compete with banks and savings institutions by offering what amounts to a checking account. For the seven-day period ended last Wednesday, major money market funds had an average seven-day interest return of 14.6 percent at a time when Treasury bills are more than two percentage points lower.

Geico is joining major stock brokerages, insurance, money management and equity fund companies in offering a money market fund. Currently, there are more than 100 of the money market investment companies, including the billion-dollar, D.C.-based First Variable Rate Fund. Geico's assets now are about $1.3 billion.

Byrne said a new subsidiary, Criterion Investment Services Co., will be the sponsor of Geico's fund. GTC Management Inc., a subsidiary of Philadelphia's Girard Bank, will act as money manager and provide day-to-day portfolio management.

According to Dick Ollen, vice president for market development at Geico and president of the new fund, Geico will concentrate marketing on current policyholders of its major automobile insurance and finance company subsidiaries