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Yes (provided you exclude monotremes) one of the defining characteristics of a mammal is live birth, others being:

Warm blooded
internal bone structure
Hair or fur covering
in the female, milk producing glands

Source: http://www.answers.com/topic/mammal

mammal

Any member of the class (Mammalia) of warm-blooded vertebrates having four limbs (except for some aquatic species) and distinguished from other chordate classes by the female's milk-secreting glands and the presence of hair at some stage of development. Other unique characteristics include a jaw hinged directly to the skull, hearing through bones in the middle ear, a muscular diaphragm separating the pectoral and abdominal cavities, and nonnucleated mature red blood cells. Mammals range in size from the tiny shrew to the enormous blue whale. Monotremes (platypus and echidna) lay eggs; all other mammals bear live young. Marsupial newborns complete their development outside the womb, sometimes in a pouchlike structure. Placental mammals (see placenta) are born at a relatively advanced stage of development. The earliest mammals date from the late Triassic Period (which ended 206 million years ago); their immediate ancestors were the reptilian therapsids. For 70 million years mammals have been the dominant animals in terrestrial ecosystems, a consequence of two principal factors: the great behavioral adaptability provided by the ability of mammalian young to learn from their elders (a consequence of their dependence on their mothers for nourishment) and the physical adaptability to a wide range of climates and conditions provided by their warm-bloodedness. See also carnivore; cetacean; herbivore; insectivore; omnivore; primate; rodent.

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Not all. The group of mammals known as Monotremes lay eggs. A platypus and echidna are examples.