The Prince William Board of Supervisors yesterday elected Alice E. Humphries of the Woodbridge District to be 1977 board chairman.

Humphries, vice chairman last year, and Donald L. White of the Gainesville District, who was elected vice chairman, were unanimous choices.

Humphries succeeds Andrew J. Donnelly of the Dumbries District who had served as chairman for one year. Donnelly, an investment broker, said the chairmanship required too much time and he chose not to run again.

Humphries is a housewife from heavily populated southern Prince William County and White is an accountant in Manassas.

Humphries takes over with the county struggling to avoid a major property tax increase. On Monday the board cut $280,000 from its $19 million operating budget but still faces a $470,000 deficit for the fiscal year.

Donnelly said recently that the real estate tax rate may have to be raised by $1.39 per $100 of assessed value from the current rate of $4.35. The increase would amount to $139 a year on a $30,000 home. The tax rate will be set April 12.

Humphries said on Monday, "The county is facing a financial crisis that must be met with a combination of budget reductions now and a higher real estate tax rate for the coming fiscal yea r."