Her first solo album, Maria Muldaur, released in 1973, contained her hit single “Midnight at the Oasis”, which reached number 6 on the Billboard Hot 100 in 1974.
It also peaked at number 21 on the UK Singles Chart. Later that year, she released her second album, Waitress in a Donut Shop. This included a re-recording of “I’m a Woman”, the Leiber and Stoller number first associated with Peggy Lee and a standout feature from her Jug Band days. The title of this album is taken from a line in another song on the album, “Sweetheart”, by Ken Burgan.
Around this time, Muldaur established a relationship with the Grateful Dead. Opening for some Grateful Dead shows in the summer of 1974, with John Kahn, bassist of the Jerry Garcia Band, eventually earned her a seat in that group as a backing vocalist in the late 1970s. Around the same time, Muldaur met and eventually collaborated with bluegrass icon Peter Rowan.