Hi MaryPeck1:
What is the make/model of your computer, your operating system, default browser (if other than the latest Chrome v75.0.x) and antivirus name and version? Please note that you've posted your question in the Windows Vista board (Chrome has not been supported on Vista since April 2016); we'll ask the Forum Moderators to move your question to a different location in the forum if necessary.
According to the article at https://www.file.net/process/mcuicnt.exe.html the genuine McUICnt.exe (McAfee HTML User Interface Container) is a executable used in a variety of McAfee products. If you do not use McAfee as your antivirus then you might have unknowingly installed a free utility like McAfee Security Scan Plus or McAfee Site Advisor that was bundled inside an installer for the Adobe Flash Player or some other third-party program.
If you suspect you have a PUP (potentially unwanted program) like McAfee Security Scan Plus and can't uninstall it from Control Panel | Programs and Features I'd suggest running a scan with the Malwarebytes Free v3 scanner. For Win 7 and higher, download the latest available Malwarebytes Free v3 installer (currently v3.8.3-1.0.613) from https://www.malwarebytes.com/mwb-download/; for Win XP/Vista, the legacy Malwarebytes Free v3.5.1-1.0.365 is available at https://downloads.malwarebytes.com/file/mb3_legacy.
If you have a third-party antivirus like Kaspersky, Norton, etc. installed I'd suggest disabling the 14-day trial version of the Premium real-time protection features of Malwarebytes at Settings | Account | Deactivate Premium Trial (see the support article How-To: Deactivate Trial Version in Malwarebytes 3) to avoid possible conflicts with your antivirus and use Malwarebytes as a manual on-demand scanner. Run a standard Threat Scan to see if it detects any higher-risk malware or lower-risk PUPs / PUMs (potentially unwanted programs / registry modifications) like McAfee Security Scan Plus. Before running your first scan I would also suggest that you change Settings | Protection | Potential Threat Protection for lower-risk PUPs / PUMs from the default Always Detect to Warn User so you're always prompted before any lower-risk threats (e.g., browser toolbars, adware, registry cleaners and other third-party utilities, etc.) are removed just in case you want to keep them.
32-bit Vista Home Premium SP2 * Firefox ESR v52.9.0 * Norton v22.15.2.22 * MB v3.5.1-1.0.365
HP Pavilion dv6835ca, Intel Core2Duo T5550 @ 1.83 GHz, 3 GB RAM, NVIDIA GeForce 8400M GS