Former White House aide Linda Chavez officially entered the race for the Republican nomination for U.S. Senate in Maryland yesterday, saying she will wage a campaign that focuses on education, crime, defense and ways to reduce government.

Chavez, 38, who announced her candidacy on a five-stop swing through the state, was the Reagan administration's highest ranking woman until she resigned last month as White House director of public liaison. She will face former Easco Corp. executive Richard B. Sullivan of Baltimore in September's primary.

"The people of Maryland have the right to know what motivated me to leave the prestige and power of the White House," said Chavez, who was flanked by her husband and three sons. "I did so because I believe that the children of Maryland, including my own three children, deserve schools in which they will learn to read and write and be honest and loyal citizens . . . . "

Chavez, a former Democrat who switched parties a year ago, said a major goal of elected officials must be to "restore traditional values to public schools." But she said she does not support a constitutional amendment to require prayer in schools, an issue that has become a political litmus test in some conservative GOP circles. "I believe that this is a pluralist society, and for that reason I do not favor a constitutional amendment that would allow prayer in schools," said Chavez.

Chavez said she would take a "hard-nosed approach" to crime, including support of the death penalty. "I want law enforcement officers to have the tools to apprehend criminals and to prosecute them," said Chavez. She called for swift sentencing and the appointment of judges "who understand that it is their role to protect society from the vicious and the unjust."

Chavez said she favors promoting economic growth by lowering individual and corporate taxes and reducing the deficit by transferring many government activities to the private sector, a concept embraced by the Reagan administration.

As an example, she said she supports the Reagan administration's plan to help cut federal spending by selling National Airport to a regional authority consisting of representatives from Maryland, Virginia and the District. That position puts her at odds with Maryland Democratic Gov. Harry Hughes and other state officials, who have argued that putting National under control of the states could place Baltimore-Washington International Airport at a competitive disadvantage.

Chavez also endorsed Reagan administration requests for an increase in defense spending, and for military aid for U.S.-backed rebels fighting the government in Nicaragua. All three announced Democratic candidates have opposed aid to the contra rebels.