Viral load as a factor is more important than condom use.
Viral load determines how infectious bodily fluids are. Levels are highest in someone who is recently infected (up to 40 million copies in a millilitre of blood). By comparison, someone on treatment with an undetectable viral load has less than 50 copies/mL (see page 17 for Figures 2 and 3). 
When viral load is very high, normally low risk activities like giving oral sex become a higher risk.
The risk of transmission from sex without a condom is dramatically reduced when an HIV positive person has an undetectable viral load.
Several studies have reported the risk to drop by more than 92% [1, 2].
The single transmission in each study occurred when the positive partner had only just started treatment when their viral load was still high.
In 2016, the PARTNER study reported no linked HIV transmissions when viral load was undetectable. This was in 900 couples who had sex more than 58,000 times without using condoms. 
Importantly, this study included gay couples and anal sex (gay and straight).
It also included periods when viral load was likely to blip between tests and times when there were other documented STIs.
Figure 2 – Viral load levels as HIV infection progresses
Figure 3 – The relationship between viral load and HIV transmission in Rakai Study 
NOTE: Person years is used when calculating risks. It allows for all the time that different people contribute to a study, even when this might be years for one person and only months for another.
- Donnell D and others. Heterosexual HIV-1 transmission after initiation of antiretroviral therapy: a prospective cohort analysis. Lancet. 2010;375(9731):2092-8.
See report from first conference presentation here.
- Cohen M and others. Prevention of HIV-1 infection by antiretroviral treatment. NEJM. N Engl J Med 2011; 365:493-505. DOI: 10.1056/NEJMoa1105243. (August 11, 2011).
- Quinn TC and others. Viral load and heterosexual transmission of HIV type 1. Rakai Project Study Group. New England Journal of Medicine 2000; 342: 921-929.
- Rodger AJ et al for the PARTNER study group. Sexual activity without condoms and risk of HIV transmission in serodifferent couples when the HIV-positive partner is using suppressive antiretroviral therapy. JAMA, 2016: 316(2):1-11. (Free online).
- i-Base report: ZERO: no linked HIV transmissions in PARTNER study after couples had sex 58,000 times without condoms. HTB July 2016.
- i-Base Q&A on the PARTNER study: how to interpret the zero transmission results
1 June 2016