Fausta Felicitas is an ancient Roman Goddess of good fortune and lucky happenstance. Her name is essentially two words of the same meaning, likely doubled up for emphasis, for fausta in the Latin is the adjective "favorable" or "auspicious", while felicitas is the noun meaning "luck", "good fortune" or "happiness"; Her name can be translated as the nicely redundant "Lucky Luck", though "She of Auspicious Good Fortune" probably sounds better. (By the way, the Latin felix, "happy", and felis "cat" are related, through the theme of "fruitfulness", as cats have many young; I'm tempted, however, to interpret the connection as referring to purring, an obvious and defining feature of happy cats). Her name evokes the Latin saying Quod bonum faustum felix fortunatumque sit!, which translates as "May it be good, lucky, happy, and blessed!" According to Cicero (who lived 106-43 BCE), this phrase had been used since ancient times as the proper ritual formula said at the beginning of all kinds of projects or events to assure an auspicious outcome—for example, when cities or colonies were founded, at public rites, at the opening of festivals, or at sacrifices.
Fausta Felicitas was also known simply as Felicitas, and as such was considered a protective Goddess of peace and prosperity. Lucius Licinius Lucullus*, a Roman general of the 2nd-1st centuries BCE, had a temple built to Her in the Velabrium, the marketplace between the Roman Forum and the Forum Boarium on the Vicus Tuscus, the main road that ran through the Velabrium connecting the Roman Forum and the Circus Maximus. This temple was decorated with quite a few statues stolen from Greece, including a set of Muses and a Venus (properly an Aphrodite, actually) by the famous sculptor Praxiteles. Lucullus must have been something of a devoté of Felicitas's, as after another military success (this one against Mithridates VI, King of Pontus, a lovely man famed both for his ability to hold his liquor and the murder of his own mother) he vowed a statue to Her. Unfortunately, though, both Lucullus and the sculptor he had hired died before it was finished.
Felicitas had another temple in Rome, this one supposedly somewhere in the northwestern end of the Roman Forum. Julius Caesar had vowed to build it in the early part of the year 44 BCE, but, since he was also assassinated in the early part of the year 44 BCE, it was actually built by one Lepidus (so much for Caesar's good luck and happiness). This temple was constructed on the site of the Curia Hostilia, or the old Senate house, which had been rebuilt after a fire eight years previous. For some reason, though, this new old Senate house was not up to snuff, and was torn down to make way either for the temple of Felicitas or for a new and improved Senate building. At any rate, the new Senate building was built in more or less the same place by Augustus several years later. No trace of Her temple remains today and it's not even sure it was ever built. The original Curia was said to have been built in the time of Tullus Hostilius, the legendary third King of Rome (who traditionally ruled 672-640 BCE), and was an inaugurated templum, or site that had been consecrated according to ancient ritual; I find it odd that, given the Roman conservatism towards things ancient and holy, anything other than a new Curia would be considered proper for that site, though my cynical side wonders if, at that particular time in which the Republic had been dissolved and rule by Emperor was beginning, the Senate was no longer considered worth bothering with.
Fausta Felicitas did have a small shrine (or altar) on the Capitoline Hill, and was worshipped there besides the shrines (or altars) of Venus Victrix ("Conquering Venus", evidentially a victorious form of that Goddess) and the Genius Populi Romani, the guardian spirits of the people of Rome. The three of them were given sacrifices on the ninth or Kalends of October, though why They should have been grouped together is a little hazy. Perhaps They were together to ensure that both the spiritual and physical aspects of Rome and her people (represented by the Genius Populi Romani) should remain victorious and secure in their sovereignty and dominance (represented by Venus Victrix), through continued good luck and fortune (represented by Fausta Felicitas).
Felicitas was shown on coins of the Empire in a variety of poses, usually holding the caduceus, or herald's staff (an attribute of Mercury or Hermes, said to represent peace) and the cornucopia, or horn of plenty. She could also be depicted holding a patera (offering dish), or with a rudder, ship's prow, or globe, all of which are also attributes of Fortuna. On these coins She was, like many Goddesses representing personified virtues, coöpted by the reigning Emperor for propaganda purposes, to imply that he cared about or brought the happiness or felicity of his subjects. As such She could be called Felicitas Deorum ("Luck of the Gods"), Felicitas Perpetua ("Everlasting Happiness"), Felicitas Republicae ("Fortune of the State"), Felicitas Romanorum ("Success of the Romans"), Felicitas Saeculi ("Happiness of the Age"), or Felicitas Temporum ("Luck of the Times&").
*say that ten times fast!