IN 1986, the Virginia state government's ability to collect child support payments from noncustodial parents was an embarrassment. An average of just $75 per family per year in delinquent payments was retrieved, leaving Virginia near the bottom nationally -- behind Guam, Puerto Rico and every state except Oklahoma. Fortunately, there is good news for single-parent households who are legally entitled to child support. Virginia, finally, is beginning to improve.

The state's Child Support Enforcement Division collected an average of $179 from noncustodial parents in 1987, good enough to move Virginia into 42nd place. Enforcement officials were a bit more efficient as well, collecting $2.23 for every dollar spent in administrative costs -- instead of just $1.57. But much more improvement is required. The Virginia House of Delegates can help by passing a bill that has already gained approval in the state senate.

The bill would authorize the Child Support Enforcement Division to have employers automatically withhold child support payments from the paychecks of noncustodial parents who have refused to pay. The senate bill would also give the division subpoena powers over financial rec-ords, making it more difficult for delinquent parents to hide assets. State officials say the law could increase collections by $20 million.

Virginia, moreover, is under federal orders to improve child support collections to offset the welfare costs of paying families through the federal Aid to Families with Dependent Children program. The state has collected so little that it faces $10 million in federal penalties for fiscal years 1984 through 1988. Federal law also requires that paternity be established in 75 percent of all public assistance cases. Virginia managed just 42 percent in 1986.

State officials say that each of Virginia's 155 child support investigators has 1,500 problem cases. Gov. Gerald Baliles is adding 188 new staff positions to allow more time on each case, and a new computer system that will monitor child support payments is being tested. Passage of a law that would provide for automatically withholding child support payments from the paychecks of delinquent parents would be a further step in the right direction.