The All-Pervading Divinity
In the classic text, the Brihat Parashara Hora Shastra, the Sage Parashara frequently recommends the recitation of the Vishnu Sahasranam, the thousand names of Vishnu, as the best remedial measure for planetary afflictions. Vishnu means "the all-pervading Divinity." See the following verse:
"The most effective and beneficial remedial measure for the prolongation of longevity and to obtain relief from other evil effects is recitation of Vishnu Sahasranam." ch 56 verse 30
Sage Parashara mentions this practice on at least 10 different occasions in his text. Here's another verse:
"The remedial measure to obtain relief from the above evil effects, is recitation of Vishnu Sahasranam." ch 59 verse 77
Sri K.N. Rao is also a strong proponent of this practice. Not only does he recite it everyday himself but he regularly recommends it to clients.
Traditionally, students of Sanskrit were often required to memorize the Vishnu Sahasranam. It takes about 20 minutes to recite depending on the speed of recitation. While recitation is preferred, just listening to the recitation by an audio recording also gives great benefit. Another form of practice is to read the text along with the translation so that the meaning also becomes integrated. Another practice is just to take one name and meditate on it's meaning. For instance, the first of the thousand names is "Vishvam" which translates as "the All," and one could contemplate the meaning of this name as a meditative practice.
The Vishnu Sahasranam was mentioned in the great epic text TheMahabharata. The 1000 names were handed down to Yudhisthira by sage Bhishma while he was on his death bed at the battle of Kurukshetra. Yudhisthira asked Bhishma the following questions:
1. Who is the one Lord of all in this universe?
2. What is that one supreme goal which one should seek to attain?
3. Who is the one Divinity by praising and by worshiping whom a man attains good?
4. Which is that highest form of Dharma that is capable of bestowing salvation and prosperity on man?
5. What is that by reciting which any living being can attain freedom from cycle of births and deaths?
Sage Bhishma answered by stating that mankind will be free from all sorrows by chanting the Vishnu Sahasranam. He said, "That man who hears the names every day or who recites them every day, never meets with any evil either here or hereafter." This quote suggests that it's not necessary to recite the sahasranam oneself to get the benefit, but can simply be listened to on an audio recording.
There are many sahasranam hymns (thousand names) to various deities like the Sri Lalita Sahasranam or the Shiva Sahasranam, which Sage Parashara also recommends in the Brihat Parasahara Hora Shastra. But of all remedial measures like puja (worship), yagya (fire ceremony), mantra recitation, giving charities, he gives primary importance to the Vishnu Sahasranam.
See the transliteration of Vishnu Sahasranam